tribological studies on the surface of glasses by lateral
TRANSCRIPT
Tribological studies on the surface of glassesby lateral indentation technique
Dissertation
zur Erlangung des akademischen Grades Doktor-Ingenieur
(Dr.-Ing.)
vorgelegt dem Rat der Chemisch-Geowissenschaftlichen Fakultaet
der Friedrich-Schiller-Universitaet Jena
Elham Moayedi
Geboren am 17.01.1982 in Teheran
Dissertation, Friedrich-Schiller-Universität Jena, [2021]
Reviewers:
1. Prof. Dr. Ing. Lothar Wondraczek, Otto Schott Institute of Materials
Research, Friedrich Schiller University of Jena
2. Prof. Morten Mattrup Smedskjaer, Department of Chemistry and Bio-
science, Aalborg University
Date of defense: 14.07.2021
Acknowledgements
First and foremost, I would like to express my sincere gratitude to Prof.
Dr. Lothar Wondraczek for his guidance throughout this thesis, for valuable
discussions and for providing outstanding opportunities for collaborations.
By the chance he gave me, I noticed how much I love research and learning
new skills and topics.
I gratefully acknowledge �nancial support from the European Research
Council (ERC) under the European Union's Horizon 2020 research and inno-
vation program (ERC grant UTOPES, grant agreement no. 681652) as well
as Starting Ramp scheme of Priority Program of the German Science Foun-
dation, �Topological Engineering of Ultra-Strong Glasses�(DFG SPP1594).
Within said ERC grant UTOPES; my work pro�ted immensely from collab-
oration with Prof. Dr. Enrico Gnecco. I am very grateful for his support
and discussions. Special thanks to Jana Henning. As part of her own Ph.D.
thesis she carried out AFM measurements.
Furthermore, I would like to thank my colleague René Limbach for valu-
able help with indentation experiments, inspiring discussions and outline of
this thesis, Peter for the hours of calculations and estimations of some data,
Ferdinand (former) for the support with OriginLab, Jan with image process-
ing, Gohar with literature providing, Shigeki (former) for all the precious
scienti�c discussions and reviewing my publication. For all scienti�c discus-
sions and the good time that I spent in the institute, I would like to thank my
current and former colleagues Bruno, Guilherme, Benjamin, Aaron, Kristin,
Ali, Lenka, Theresia, Huyen, Courtney, Garth, Caio, Doris, Vivi, Yuko, Fe-
lix, Byoungjin, Lingqi, Yang, Xu, Ru, Atef, Ding, Pigter, Roman, Omar,
Jelena, Vahid, Ayda, Aziz, Thien, and Michal. My sincere gratitude to the
kindest secretary (former) Ute Böttger, and technicians Christian Zeidler,
3
4 Gutachter
Gabriele Möller (former), Nadja Büchert, Thomas Kittel (former) and Clau-
dia Siedler, for all their kindness and e�ort to support my studies.
I would also like to state my appreciation to the external collaborators
at the Leibniz Institute of Photonic Technology (IPHT), Dr. Jan Delith and
Andrea Delith for performing AFM measurements for me.
Finally, my warm gratitude to all my family and friends. Specially the
ones that helped me by their kind advice and encouragements during these
di�cult times of pandemic. I am very grateful that my beloved husband
Enrique Fernandez helped me with the Latex issues and stayed with lots of
patience on my side.
ت رون ز ه ود آ ن و ا
ق ت و ن ت دا س
د ودا ی از س
ت د ی دا س ت زآن روی
یام
Amidst this Strait which swells of Chasm’s Hide,
No salt would dare his shaky vessel guide!
Upon say-so each captain mapped a chart,
But none could tell what lies beyond the tide!
Omar Khayyam
Translated by Edward FitzGerald
5
Contents
Contents viii
List of Figures xii
List of Tables xiii
Abstract 1
Glossary 3
1 Introduction 7
2 State of the art 11
2.1 Deformation in glasses . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Formation of cracks in contact-induced damaged surface . . . 13
2.3 Parameters a�ecting deformation regimes . . . . . . . . . . . 15
2.3.1 The indenter geometry . . . . . . . . . . . . . . . . . . 15
2.3.2 The applied normal force . . . . . . . . . . . . . . . . 16
2.3.3 Scratching rate . . . . . . . . . . . . . . . . . . . . . . 17
2.3.4 The glass surface condition . . . . . . . . . . . . . . . 18
2.3.5 Environmental atmosphere and humidity . . . . . . . . 20
2.4 Compositional dependence of deformation in glass . . . . . . . 22
2.5 Contribution of friction to materials behaviour in indentation
experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
vii
viii CONTENTS
3 Experimental methodology 29
3.1 Ramp load scratching . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 Ramp load scratching test on vitreous silica . . . . . . 29
3.1.2 Scratching of metallic glass by a spherical indenter . . 32
3.2 Constant low load scratching . . . . . . . . . . . . . . . . . . 33
3.2.1 Scratching at constant load by a Berkovich indenter
on vitreous silica . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 Constant low load scratching on silicate glasses . . . . 34
3.2.2.1 Glass samples . . . . . . . . . . . . . . . . . 34
3.2.2.2 General characterization . . . . . . . . . . . . 34
3.2.2.3 Scratching and indentation tests . . . . . . . 35
3.2.2.4 AFM imaging and subsequent heat treatment 35
4 Results and discussions 37
4.1 Studies at low load scratching in plastic regime of deformation 39
4.1.1 Relaxation of scratch-induced surface deformation in
silicate glasses . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.2 Rippling inside the scratch groove of vitreous silica . . 47
4.2 Studies at ramp load scratching in plastic regime of deformation 56
4.2.1 Statistical analysis of microabrasion onset in vitreous
silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.2 Scratching of metallic glass by a blunt indenter . . . . 67
5 Conclusions 79
Zusammenfassung 83
Bibliography 108
Appendix 109
Selbstsändigkeitserklärung 112
List of Figures
2.1 Typical scratch pattern made on the surface of the Soda lime
silica glass by a vickers penetrator (leading edge) during a
monotonic loading cycle [1]. . . . . . . . . . . . . . . . . . . . 14
2.2 Maximum density relative variation after high hydrostatic pres-
sure testing at room temperature as a function of poisson's ratio. 23
3.1 Schematic of the determination of lateral load during lateral
displacement of Berkovich indenter . . . . . . . . . . . . . . . 30
3.2 a 3D representation of the employed Berkovich tip, obtained
by wide-�eld confocal microscopy. . . . . . . . . . . . . . . . . 31
3.3 The Berkovich tip edge-forward and face-forward con�gura-
tions during scanning . . . . . . . . . . . . . . . . . . . . . . . 31
4.1 (a) Typical scratch pattern which is observed on silicate glasses
during steady scratching with increasing normal load. (b)
Scratch pattern of vitreous silica observed at ramping load of
0.05-300 mN and scratching rate of 100 µm/s. . . . . . . . . . 38
4.2 Typical AFM micrograph of a scratch groove as used for vol-
ume analysis for boro�oat 33 . . . . . . . . . . . . . . . . . . 40
4.3 AFM top-views and cross-pro�le scans of the residual imprints
after Berkovich indentation, before and after annealing for 1
h at 0.95Tg, shown for silica, BF33, and SLG. . . . . . . . . . 41
4.4 AFM top-views and cross-pro�le scans of the residual scratch
grooves after Berkovich edge-forward scratching, before and
after annealing at 0.95Tg, shown for silica, BF33, and SLG. . 44
ix
x LIST OF FIGURES
4.5 (a) Cross-pro�le data of scratches on SiO2 before and after
annealing at 0.95Tg for 1 and 2h. (b) Recovery ratio versus
annealing time for di�erent scratch rates. . . . . . . . . . . . 45
4.6 Cross-pro�le scans over a scratch groove on BF33 before and
after 1h annealing at 0.95Tg for face-forward and edge-forward
orientation of the Berkovich tip. . . . . . . . . . . . . . . . . . 46
4.7 Recovery ratios as a function of (a) loading values and (b)
Poisson's ratio for normal and anomalous glasses. . . . . . . . 47
4.8 An atomic force microscopy image of a part of one scratch
performed at scratching rate of 10 µm and increasing normal
load of 10 mN showing ripples in the scratch groove. . . . . . 48
4.9 (a) AFM topography of a silica glass surface previously scratched
with a normal force of 30 mN and a scan velocity of 10 µm/s.
Set point: FN = 1.8 mN. (b) Cross section along the light
blue line in (a). (c) Simulated herringbone pattern obtained
from the simple repetition of Berkovich geometry. (b) Cross
section along the light blue line in (a). (c) Simulated herring-
bone pattern obtained from the simple repetition of Berkovich
geometry every 350 nm without relaxation e�ects. . . . . . . . 50
4.10 (a) AFM error signal across the wear scar in Fig. 4.9(a). (b)
2D self-correlation and (c) 1D-FFT along longitudinal direc-
tion extracted from the region corresponding to the herring-
bone pattern in (a); (d), (e) cross sections along the blue lines
in (b) and (c), respectively. . . . . . . . . . . . . . . . . . . . 51
4.11 Laser scanning microscopy image of a wear groove obtained
in the same conditions of Fig. 4.9(a). . . . . . . . . . . . . . . 52
4.12 Velocity dependence of the ripples period as measured by
AFM ex situ after scratching with a normal force FN = 30
mN (blue dots) and linear �t of the experimental data points
(red curve). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.13 (a) Time variation of the indentation depth while scratching
with v = 10 µm/s. (b) Lateral force vs. indenter position
when the scratching process initiates (at x = 20 µm). . . . . . 54
LIST OF FIGURES xi
4.14 Evolution of lateral force during scratching while increasing
the normal load from 0.05 mN to 300 mN at a scratching
velocity of 500 µm/s. . . . . . . . . . . . . . . . . . . . . . . . 58
4.15 (a) Scratch pattern for fused silica at a scratching rate of 50
µm/s and a normal load which increases from zero to 300
mN, using an irregular diamond edge for scratching. (b) is a
representation of the corresponding variation in the apparent
friction coe�cient. . . . . . . . . . . . . . . . . . . . . . . . . 59
4.16 Determination of the onset of microabrasion (scratch length in
µm) OM through di�erent methods: (a) Post mortem optical
microscopy and in-situ observation of the apparent coe�cient
of friction, and (b) optical microscopy and in-situ observation
of the lateral force. In (c) the determination of lateral force
is considered, i.e., as read directly during in-situ scans and
as determined from the length at which OM was observed
through the apparent coe�cient of friction, µ, according to (a). 62
4.17 Post mortem optical microscopic image of a scratch generated
at a scratching speed of 10 µm/s under increasing normal load
(3 mN/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.18 Statistical analysis of the onset of microabrasion (OM) in vit-
reous silica during lateral indentation. . . . . . . . . . . . . . 65
4.19 (a) An Scanning Electron Microscopy overview image of two
scratches performed at load of 30 mN and scratching rate of
10 µm/s. The whole scratching length is not shown in the
image. (b) A pro�le of displacement into surface over the
whole lateral length for a scratch at the same conditions. . . . 69
4.20 The normal load vs. penetratuin depth curves for indentation
(left) and scratching (right) experiments at normal load of 20,
30 and 40 mN. All scratching experiments were performed at
scratching rate of 10 µm/s. . . . . . . . . . . . . . . . . . . . 70
4.21 Normal loads at �rst pop-ins appearance for indentations and
scratching (left) and lateral loads for scratching experiments
(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
xii LIST OF FIGURES
4.22 Coe�cients of frictions for scratches at loads of 20, 30, 40 and
50 mN. Each experiment was repeated 5 times. . . . . . . . . 74
4.23 a) An image of a scratch at the load of 30 mN obtained by
Scanning Electron Microscope b) and c) Atomic force mi-
croscopy images of two marked sections of the same scratch in
(a), d) and e) Center line pro�les of AFM images in (c) and
(d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.24 Comparison of pop-in loads read from indenter and the point
of appearance of patterns in SEM images for the scratching
loads of 20 and 30 mN. An standard deviation of 5% µm
should be taken into account for the data. . . . . . . . . . . . 77
F1 (a) Width and (b) depth of the wear grooves formed on a
silica glass surface scratched by a Berkovich diamond tip with
a scan velocity of 10 µm/s and di�erent normal loads. . . . . 110
F2 (a) AFM topography corresponding to Fig. 4.10(a); (b) hori-
zontal cross-section along the blue line in (a). . . . . . . . . . 110
F3 AFM topography of the very end of the scratch. Frame size:
14.1 µm∗6.1 µm. . . . . . . . . . . . . . . . . . . . . . . . . . 111
F4 (a) AFM topography of one section of scratch performed at
load of 30 mN. (b) Pro�le along the scratch shown with a
horizontal line in (a). (c) FFT analysis of the same image.
(d) Pro�le along the line in (c). . . . . . . . . . . . . . . . . . 111
List of Tables
3.1 Glass transition temperature Tg, density ρ, Young's modulus
E, shear modulus G, bulk modulus K, atomic packing density
Cg and Poission's ratio ν of the studied glasses. . . . . . . . . 34
4.1 Indentation and scratch volumes before and after annealing
for di�erent experimental conditions. . . . . . . . . . . . . . . 42
4.2 Onset of microabrasion (OM) for a series of 20 experiments,
scratching vitreous silica at a rate of 50 µm/s with normal
load increasing from 0.05 mN at a rate of 15 mN/s. . . . . . . 64
4.3 Weibull parameters for failure modes I and II and varying
speed of scratching. . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4 Normal loads and lateral loads at which the pop-ins appear
for each experimental load at 20, 30, 40, and 50 mN. . . . . . 72
xiii
Abstract
Glass is a material particularly sensitive to surface damage when exposed to
abrasive loads and scratching. Such local mechanical contacts not only com-
promise the surface quality and mechanical performance, but also degrade
the visual appearance of material. Understanding abrasive damage and the
underlying material properties has therefore been a subject of signi�cant in-
terest. Hence instrumented lateral nanoindentation has been employed in
this thesis to obtain quantitative and quantitative information on the onset
of scratch-induced surface of three silicate glasses and one metallic glass in
low load and high load regimes. First, the role of compaction and shear �ow
in the deformation caused by lateral indentations on silicate glasses is quan-
ti�ed through classical relaxation experiments. In the anomalous glasses,
the main mechanism of plastic deformation in lateral indentations was re-
vealed to be densi�cation, while in the normal glasses, shear �ow played a
considerable role. Furthermore, lateral indentation was used to study the
appearance of wavy patterns formed by sliding on a compliant surface which
was investigated later by post mortem AFM technique. The average repeti-
tion distance of the ripples which is in the sub-µm range was displayed to be
dependent on the scratching velocity. Additionally, a correlation was noticed
between scratching velocity (loading rate) and the formation of microabra-
sion regime in vitreous silica when analysing the data through Weibull distri-
bution. The quantitative information obtained through Weibull distribution
analysis showed the considerable role of tested volume in the appearance of
di�erent types of �aws. Not only scratching velocity, but also loading can in-
�uence the deformation behaviour of glasses. This was further exhibited by
analysis of pop-in loads when performing lateral indentations on the surface
of a metallic glass.
1
Glossary
Cg Atomic packing density. 32
Er combined elastic response of the indenter tip and the glass specimen. 56
FN Normal load. 37
Ff Coulumbian friction e�ort. 25
Fk Kinetic friction force. 46
Fs Threshold value for friction force. 47
Ft Tangential force. 25
Fcr Cracking e�ort. 25
Fdef Ductile deformation e�ort. 25
Kc Fracture toughness. 23
LL Lateral load. 27
LN Normal load. 27
Mi Molar mass of the ith component. 32
Pf Probability of failure. 50
Tg Transition temperature. 30
VL Longitudal wave velocity. 30
V +R Volume ratio of pile up recovery. 39
V −R Volume ratio of sink in recovery. 39
3
4 Glossary
VR volume ratio of annealing recovery. 37
VT Transversal wave velocity. 30
V +a Pile up recovery volume after annealing. 39
V −a Sink in recovery volume after annealing. 39
V +i Initial pile up volume. 39
V −i Initial sink in volume. 39
Vi Theoritical molar volume. 32
Φ Diameter. 30
α Cutting angle of specimen. 44
β Rake angle. 25
λ Repetition distance of ripples. 44
µ Coe�cient of friction. 25
ν Poisson ratio. 30
ω The resonance frequency of the system. 47
π The ratio of a circle's circumference to its diameter. 32
ρ Density. 30
σu Threshold parameter for stress. 50
θ Apex angle. 19
fi Molar fraction of the ith component. 32
rA Shannons ionic radii of the involved ion species. 32
A Area. 46
AFM Atomic force microscopy. 24
B Brittleness parameter. 23
BMG Bulk Metallic Glass. 11
Glossary 5
COF Coe�cient of friction. 59
CSM Continuous sti�ness measurement. 32
DSC Di�erential scanning calorimetry. 30
E Young modulus. 30
EF Edge forward con�guration of tip. 53
FFT Fast fourier transformation. 44
G Shear modulus. ix, 34
H Meyer's hardness hardness. 23
h Penetration depth. 56
K Bulk modulus. ix, 34
k Lateral sti�ness. 46
m Weibull modulus. 50
N Avogadro number. 32
n Number of scratches per experiment. 50
OM Onset of microabrasion. 50
R Correlation coe�cient. 51
SEM Scanning electron microscopy. 30
SLS Soda-lime silica glass. 20
SNL Sharp Nitride Lever. 30
SSD Subsurface damage. 14
StD Standard deviation. 39
v Scan velocity. 43
x distance between two points. 46
Chapter 1
Introduction
Although some of the questions regarding the behavior of glasses under sharp
contacts have been answered in the last decades, it is still a very active topic
throughout the world's glass community, in both the academic and industrial
�elds. Considering the very outspread applications of glasses in everyday life
such as lenses, windows, monitors and touch-screen devices, surface quality
and visual appearances of employed glasses becomes an important topic. The
advances in the last 15 years in the area of more resistant glass compositions
with regard to contact-induced damage have had such prominent e�ects in
our lives that anyone with a smart phone or laptop can sense the �ourish-
ing progress. The widely used glass in ultra-sophisticated applications as
mobile devices and biomedical applications needs grinding and polishing to
the utmost precision [2�4]. Material removal in these processes is obtained
by cumulative scratching actions of multiple individual grits of random dis-
tribution, which is far from well understood [5] (e.g. frictional shear force
vector that is associated with material �ow lines in contact surface between
indenter and material [6]). On the other side, by being subjected frequently
to abrasive loads, not only the surface quality of glasses is a�ected negatively
by appearance of �aws, but also these �aws can act as stress ampli�ers and
reduce the mechanical properties of the material.
To resolve �nally the contact-induced damage issues in glasses, it is nec-
essary to take the next steps with a mechanical approach through which a
better understanding of deformation behavior of glasses under sharp con-
tact is targeted and also to determine the constitutive laws for plasticity
7
8 Introduction
and damage nucleation with respect to the structure of the glass and its
deformation under especially compressive loads. Although nanoindentation
testing has become a standard testing mean to characterize various mate-
rial properties such as elastic modulus (E), Poisson's ratio (ν), hardness (H)
and critical stress intensity factor (KIc) and all these provide good infor-
mation from the engineering point of view, they do not transcribe neither
the complexity nor the various mechanisms that take place during plastic
deformation of glasses [1,7�11]. Whence the lateral indentation technique is
used as a main method in this dissertation to extract numerous information
from the surface of di�erent types of glasses.
The scratch test is one of the fundamental techniques to evaluate the
response of material to abrasive loads under sharp contacts [12]. A scratch
is a typical surface damage that consists of visible grooves appearing as a
result of mechanical deformation [13]. The instrumented scratch test gives
access to the X-Y-Z displacements, the longitudinal one from which the
scratch velocity is computed, the lateral one (normal to the sliding direc-
tion) and the vertical displacement or penetration depth into the surface
and to the corresponding forces (Fx, Fy, Fz), the tangential force (sliding
direction), the lateral one and the applied normal force, respectively [14,15]
and from here it is possible to characterize the material in term of scratching
hardness, wear properties, fracture toughness, materials strength, scratch-
ing behaviour of coatings, adhesion and bond strength between a �lm and
substrate [4,16�23]. However, scratching is a more severe deformation mode
than indentation. Because di�erent factors such as shear-induced deforma-
tion, stick-slip reactions and frictional shear stress/adhesive force are more
likely to give rise to a fully plastic regime [4, 24].
Despite the fact that there are established protocols for scratch testing,
these protocols provide only qualitative information. Among these investi-
gations, the distinct regimes of damage in some types of glasses have been
studied [7,25]. However, A broad variety of parameters determines this phe-
nomenology, including the rate of scratching, the indenter geometry relative
to the scratching direction, the applied normal force, glass surface conditions,
environmental atmosphere and humidity, and the presence of debris or impu-
rities on the specimen surface. So far, the concrete action of these parameters
has received only very limited attention [1, 26, 27]. This is particularly the
case for the technically relevant question of compositional dependence which
Introduction 9
has been the motivation of the study in section 4.1.1. Using lateral nano-
indentation within the plastic regimes of silica, borosilicate and soda lime
silicate glasses, an insight is given to the role of densi�cation and shear �ow
in overall permanent deformation of studied glasses.
In addition, we know that the normal indentation experiments on brit-
tle materials usually ignore contributions of friction [28] or stick-slip reac-
tions [29]. This leads to fundamental di�erences in material behavior during
normal hardness testing or in lateral contact situations [30]. So far, only lim-
ited attention has been given to this topic in the �eld of glass. From here, a
special focus was set to understand the fundamental relation between stick-
slip phenomena and topography of the scratch grooves in vitreous silica and
the related results are discussed in section 4.1.2.
Surprisingly, vitreous silica with its attractive properties such as low
thermal expansion, low poisson's ratio and high free volume has not been
studied in term of tribological properties widely and almost all so far studies
focus on the phenomenology of deformation behavior of this material. This
shortage was approached by analysing the quantitative information which
can be obtained by statistical analysis of lateral force data during scratching
of vitreous silica. The results of this study are presented in section 4.2.1.
After all, even considering the valuable properties of inorganic glasses
that make them in the modern-day world widely used where transparency,
luster, and durability of glass is needed, they are not functional in some
new industrial applications that need a combination of high resistance to
wear, high yield strength, high bio-compatibility, and being at the same
time highly deformable. Metallic glasses seem to be in this direction inter-
esting candidates and have been gaining considerable attention in the last
years. For all that, their mechanical properties have been the focus of many
studies [31�37]. But the dynamical behavior of nano-scratching in these ma-
terials has not obtained much attention. For this reason, the response of
one metallic glass under lateral indentation is investigated. The results in
section 4.2.2 show the clear role of loading in the formation of shear bands
and the di�erences that exist between lateral and normal indentations.
Chapter 2
State of the art
2.1 Deformation in glasses
The juxtaposition of two words plasticity and glass may sound incongruous or
strange, since mostly glasses are considered the archetype of materials having
a brittle behavior. However, because of diverse composition, structure and
bonding nature of glasses (from metallic to covalent), not all types of glasses
are having the same kind of permanent deformation. For example, while
oxide glasses experience a brittle fracture being exposed to tensile stresses
and being far from the transition temperature, metallic glasses (bulk metallic
glasses; BMG) act in a similar way as metallic alloys, exhibiting a large
amount of plastic deformation before fracture happens when being tested
under tensile conditions [15,38].
In oxide glasses, the deformation can be the result of atmospheric cor-
rosion, as a result of devitri�cation at surface inhomogeneities or at inho-
mogeneities in the volume where the formed crystalline inclusions produce
cracks by mis�t stresses, or as a result of mechanical contact with sharp
objects. It has been recognized for some time now that the �free volume
�, which refers to the fraction of matter having a lower atomic coordination
than that in a reference material having a dense random packing of molecules
or chains of molecules and the same composition, is of key importance to un-
derstand the deformation of oxide glasses. In these free volume regions the
mechanical coupling to the surroundings is weak and this makes the inelastic
relaxations possible by local atomic rearrangements or molecular segment ro-
11
12 State of the art
tations without signi�cantly a�ecting the surroundings. On the other hand,
through the study of the kinetics of the linear viscoelastic behavior of glasses
of all types under low stress, it has been established that such local relaxation
processes are not mono-energetic but are characterized by a wide spectrum
of activation energies that correspond to a wide gradation of free volume
sites with di�erent local coordination [38].
Now, if we regard the behavior of glass under compression, it is totally
a di�erent story. Nowadays, permanent imprints left on the glass surface by
indentation are a well-known technique to study the behavior of glass under
compressive loads [15]. The �rst traces of such permanent imprints on the
surface may have been found in relation to sleek. A type of impression on
the surface that looks like a scratch rather than fractured sharp fragments.
J.W. French [39] attributed this residual imprint to the Beilby layer (for
more information on Beilby layer see [40]), or surface �ow layer, generated
by polishing, rather than to the bulk glass which has a brittle behaviour in
the nature [15].
Later Taylor announced that a diamond tip can make permanent, crack-
free indentations in glasses. Taylor in the same year performed such perma-
nent marks on the glass surface by sharp vickers or cube like shaped diamond
tool under small loads and explained them as a result of partly plastic defor-
mation [41]. Finally, Bridgman and Simon studied the mechanical properties
of oxide glasses and showed that they can be permanently compacted and
under enough high pressure some short and middle range structural rear-
rangement will occur [42]. Nowadays, scratching of glass by a hard point is
a well established method to measure di�erent characteristics of glasses as
strength, scratch hardness, wear and damage, fracture toughness, adhesion
strength and bond strength between the �lm and substrate [4, 43].
As pointed, the relationship between structural changes and loading was
studied by Bridgman and Simon who showed that for su�ciently high pres-
sure, oxide glasses experience structural rearrangements at the short- (coor-
dination number, tetrahedral to octahedral) and medium-range order (inter-
tetrahedral bond angle Si-O-Si, n-fold rings statistics). They also showed
two important pressure thresholds: the pressure to start the densi�cation
process (around 10 GPa for silica) and the pressure for saturation of densi�-
cation (near 20 GPa for silica). Between these two thresholds the permanent
2.2. Formation of cracks in contact-induced damaged surface 13
densi�cation of glass increases by increasing the pressure. By x-ray measure-
ment, almost no modi�cation of the short-range order (Si-O bond distance)
was observed in the densi�ed amorphous phase, which was attributed to an
atomic-scale mechanism leading to some sort of local folding of the glass
network upon compression [15,42].
Now it is well known that after applying load on the glass specimen, it
initially undergoes elastic deformation which has two hydrostatic and shear
component. By removal of the load, the material returns to its original
dimensions. By applying the stress beyond the yield point of the material, it
does not return to its original dimension. In this state, the hydrostatic stress
component densi�es the glass under the load, whereas the balance of shear
stress component causes the glass to undergo plastic deformation [44,45].
2.2 Formation of cracks in contact-induced dam-
aged surface
Contact-induced fracture has been studied now for more than a century.
Hertz [46] was the �rst to study the cone crack formation under loading by a
spherical indenter. These were named Hertzian cracks after him. But it was
only in the 1950s that scientists started to study the fracture mechanisms
under contact loading, trying to decipher when, how and where the cracks
initiate.
For pyramidal indenters, and more speci�cally for Vickers indenters (squared-
based pyramid), two di�erent principle cracking systems do develop in inden-
tation experiments. The �rst one is called the radial/median crack system:
median cracks are the �rst cracks to appear under the loading and parallel
to loading axis. Median cracks nucleate below the plastic deformation zone
under the load. They do need a certain load threshold in order to nucleate.
Then they propagate in a stable way as the load increases; they have a cir-
cular shape. The radial cracks are inclined toward the sliding direction and
have a curved shape and propagate perpendicular to the scratch direction
and emerge from the edge of plastic contact impression and remain close to
the surface. Lateral cracks are subsurface cracks that form during loading
at higher loads (than median and radial cracks) and propagate during un-
loading. They form beneath the deformation zone and run quasi-parallel to
14 State of the art
the sample surface. When they merge to the surface, they form chips that
may detach from the surface [25,47,48]. With mentioned studies, it became
easier to understand the deformation regimes that take place in scratching
experiments. However, scratching is in some ways a more natural aggression
of a surface, yet it is even more complex and di�cult to understand than
the indentation test. The main di�erence of scratching experiment with in-
dentation is that the indenter is slid onto the surface while a normal load is
applied, thus increasing the shear strain.
Ahn et. al. [49] stated that in scratching experiments on soda-lime silica
glass di�erent cracking systems appear: (I) the �rst regime takes place at
loads of 0-50 mN, where a hardly visible to the naked eye plastic tray (no
cracks) is left behind at the surface. Le Houérou and colleagues [1] later
called that a microductile regime, where the radial (chevron) cracks are the
�rst �aws that appear and subsurface lateral cracks form under plastic track
in a permanent groove (Fig. 2.1).
Figure 2.1: Typical scratch pattern made on the surface of the Soda lime
silica glass by a vickers penetrator (leading edge) during a monotonic loading
cycle [1].
(II) By increasing the load, shallow lateral cracks on the sides of the
plastic groove will appear, forming a chevron-like pattern. Then, as they
grow in size with increasing load, median cracks will form underneath the
groove perpendicular to the surface and parallel to the scratch direction.
This was called the the micro-cracking regime and �nally (III) microabrasive
2.3. Parameters a�ecting deformation regimes 15
regime takes place where debris form and the material is removed from the
surface [1, 49].
2.3 Parameters a�ecting deformation regimes
The most in�uential parameters a�ecting the scratching behaviour of glass
have been investigated by di�erent researchers. Glass composition, load
level, loading speed, thermal treatment history, humidity, indenter geometry
and the glass surface conditions have been mentioned as the most prominent
factors that in�uence the damage in glasses [7,9,50,51]. In the next section
some of these parameters and their in�uence on the deformation of glass will
be discussed.
2.3.1 The indenter geometry
Many investigations have shown that the development of the cracking sys-
tem depends strongly on the indenter geometry. Not only the angle, but also
the radius and the shape of indenter a�ect the critical conditions for crack
growth [26, 52�54]. It is now established that there are two basic types of
indentation fracture pattern, depending on whether the contact is essentially
elastic (�blunt�indenters) or plastic (�sharp�indenters) [55]. The blunt inden-
ter a�ects more visible scratches on the glass surface, whilst sharp indenters
grate the surface and produce �ner and more homogeneous scratches [56].
As contacts become sharper, the plastic deformation transitions toward the
shear deformation. On the other words, the blunter contacts tend to create
more densi�cation e�ect. Blunt indenters are also useful, specially at low
loads and when measuring the tribological properties of material in elastic
zone is favoured. Here by increasing the load, the response of material in the
transitional elastic/plastic zone and fully plastic zone can also be probed [57].
Lawn and Evans (1977) calculated that the critical load for fracture of
glass from a sharp indenter is 0.02 N, much less than that required for impact
of a spherical particle (for example, 0.4 mm radius particle requires 98.5
N) [58]. Veldkamp reported that in the case of ideally sharp indenters, micro-
ductile regime takes place immediately after the application of a load below a
certain semi angle of the point [52]. Schneider found that while the diamond
cone indenter with 600 tip geometry produces mostly a micro-abrasive regime
16 State of the art
for soda-lime-silica glass, the Ritz diamond indenter produces scratches in
micro-ductile regime.
Experiments with face forward or edge forward orientation of tip can
also a�ect the cracking behavior of glasses. For example, Veldkamp [52] ob-
served that the length of the median cracks obtained during scratching of a
64.9SiO2.12.3BaO.6.2K2O3.2Al2O3.1.8CaO.1.1MgO.0.55b2O3.0.2SrO.0.2CeO
glass with a face forward orientation of tip were about a factor 2 lower than
those found by Peter [59], who used a leading edge indenter in his experi-
ments.
2.3.2 The applied normal force
Load dependence of scratching behaviour of silicate glasses has been dis-
cussed by various researchers and it has been shown that the appearance of
cracks is load dependent [26, 38, 52, 53, 60�65]. Auerbach [66] showed that
there is a critical load at which the glass starts the cracking [67]. This was
further con�rmed in the experiments of Marshall [60].
The scratch pattern also strongly depends on the level of the normal load
and di�erent types of cracks appear due to the loading level (as shown in Fig.
2.1). Bensaid et al. [68] studied the e�ect of loading on the scratch pattern in
a soda lime silica glass. They found that at load of 0.1 N only median cracks
appear, from 0.3 N to 0.7 N lateral cracks initiate and propagate inside the
material without intersecting the surface, Beyond 1 N until 2 N lateral cracks
were intersecting the surface and resulted in chips growing while increasing
the load, all these in con�rmation with the observations of Veldkamp [52].
They additionally observed that the micro-abrasive phenomena was occur-
ring at the end of the scratch due to the plowing of the indenter with glass
debris (chips and fragments).
The spatial extent and the number of damage increases with increasing
the load [52]. For example, Gu [63] reported that the scratch depth and
damage zone size (It was assumed that the size of the damage zone is induced
by lateral cracks) increases in BK7 glass with increasing the applied normal
load when sliding a vickers indenter on the surface. Marshall showed that
the lateral crack length increases with increasing the normal load on the
surface of Soda-lime silica glass [60]. It has also been con�rmed that the
residual �eld provides the driving force for crack evolution and the residual
2.3. Parameters a�ecting deformation regimes 17
�eld is related to the loading. The principal stress and the residual stress
�eld beneath the indenter were studied by many researchers for glass and
ceramics [69�72].
2.3.3 Scratching rate
The results of studies performed by various researches show a relationship
between damage-induced surface and scratching speed. The type and extent
of such damage has been discussed in di�erent investigations [26,38,52,53,73�
76]. Peter [59] found that the depth of the cracks experimentally decreases
with increasing scratching speed.
Bandyopadhyay et al. [76] investigated the e�ect of scratching speed (100,
500 and 1000 µm/s) with a Rockwell C diamond indenter on the scratching
behaviour of a soda-lime-silica glass. He showed that more surface but less
sub-surface damage is induced to the glass surface at lower scratching speed
as a result of higher maximum shear stress at higher scratching speeds. He
explained this as a result of smaller contribution of shear stress just under-
neath the indenter. Furthermore, an inverse law dependency was observed
between scratch width, depth and wear volume and scratching speed for a
given applied load. That means for any applied load, the scratch width was
highest at lowest scratching speed and lowest at highest scratching speed
due to higher time of contact between the scratching indenter and the glass
surface. Also, the number of Hertzian tensile cracks and the microdamage
inside the scratch grooves reduced with scratching speed. For higher veloc-
ities, the interaction among Hertzian tensile cracks and the microdamage
inside the scratch groove were lower. Besides, At higher applied loads of
10 and 15 N micro-chip formation, as well as micro-wear debris formation
occurred and the degree of their occurrences were more signi�cant at lower
scratching speeds (e.g. 100 µm/s) than at higher scratching speeds. Another
consideration in these experiments was the relationship between shear bands
formation and scratching speed. At higher loads where the shear bands ap-
peared, they were mutually perpendicular to each other at scratching speed
of 100 µ/s, while at a higher scratching speed of 1000 µm/s the shear bands
were oriented at small angles with respect to the direction of scratching and
also with respect to each other [76].
18 State of the art
Li and his colleagues performed a series of scratches on the surface of
Soda-lime silica glasses using three conical spherical indenters (3 mm tip
radius) with 60, 90 and 136 °apex angles (2θ) under a normal load of 10
g and scratching speeds of 2, 3, 4, 5, 7, 10, 20, 50, 100 and 200 µm/s and
measured the depth and width of scratches by atomic force microscopy. They
noticed that the scratch grooves decreased with the increase of speed. For
the 90 °indenter, the crack density (de�ned as the fraction of the scratch
covered by cracks) decreased with increasing speed. This was explained by
nucleation theory: Since a crack has to be nucleated from the scratch, it may
take some time which depends on the local stress concentration based on the
usual heterogeneous nucleation theory. After a crack has been nucleated
and propagated the stress concentration is reduced so the next crack cannot
be nucleated until the stress concentration is built up again. From here by
increasing the scratching speed, the probability of cracking is reduced based
on both of these considerations. They estimated the relationship between the
crack density and scratching speed based on �rst order kinetics and showed
that the probability of cracking is proportional to the available uncracked
area of the scratch and the faster indenter moves, the bigger becomes the
uncracked area.
This relationship was also observed by Klecka et al. [74] in the way that
the faster scratch speed contributed to the increased propagation of lateral
cracking around the edges of the scratch, resulting in further material re-
moval. Both studies con�rm the observations of Veldkamp (1978) [52] that
number of cracks per unit length of scratch decrease with increasing the
speed of sliding. However, it has been shown that when the crack density
was low or when the separation of cracks exceeded a certain distance, the
interaction between cracks no longer played a role so the density of cracks
became independent of scratching speed or it was assumed that it depended
on speed in a di�erent way. The coe�cient of friction (the horizontal to
vertical force ratio) was shown to be independent of scratching speed in the
range of their experiments [73].
2.3.4 The glass surface condition
The topic of glass surface is very wide and consists of chemical and physical
reaction of environment with glass, surface tensions and relaxation, topog-
2.3. Parameters a�ecting deformation regimes 19
raphy, the presence of debris, particles on the surface from polishing or pro-
duced by applying load on the surface and so on. In fact, the glass surface
condition could be itself a independent topic of investigation. But discussing
all various aspects of glass surface is not within the scope of this work and
hereafter, only some facets that are in relation to our investigations will be
considered here.
Any material interacts with its environment through its exposed surface.
The physical and chemistry status of a bulk glass is not necessarily trans-
ferable to the bulk glass and hence, characterization of the glass surface
presents unique challenges and opportunities [77�79]. The manufacturing
process can a�ect the structure of glass surface dramatically. Surface �aws
produced by machining or handling are the predominant source of failure in
glass [80]. From here, the engineering of glass surfaces could also provide
the next breakthroughs in glass technology, for example, in the design of
glasses with special surface properties such as high chemical durability, high
damage resistance, self-cleaning properties, or other types of functionalized
surfaces. Nearly all oxide glass surfaces are almost immediately hydroxy-
lated by exposure to a humid environment which was explained in section
2.3.5 [79].
The presence of impurities, debris, microscopic cracks makes the glass
more vulnerable to unwanted deformation. The microabrasive phenomena
occurring at the scratching process is due to the plowing of indenter with
glass debris and the chip formation is reported to be as a result of shear-
induced microcracks generated in the sub-surface region of some glasses (for
example SLS) (chips and fragments). Thus, the polishing processes and
materials can also have a strong in�uence on the surface quality of glasses.
Veldkamp [52] observed more lateral cracks on the mechanically polished
surface of glass rather than �ame polished one [7, 27, 63, 68, 76]. When such
microchips fall in between the sliding indenter and the scratch groove, they
are further comminuted to form the micro wear debris which get entrapped
in between the sliding indenter and the scratch groove, and enhance the
coe�cient of friction [44,81].
20 State of the art
2.3.5 Environmental atmosphere and humidity
Another parameter a�ecting the deformation regimes of glass is humidity.
It is believed that humidity can a�ect the glass through a stress-enhanced
chemical reaction between a chemical environment, usually water, and the
Si-O-Si bonds. From here, it has been reported that the water environment
promotes the crack initiation in silica, pyrex type glass and soda-lime glass
[82, 83]. Since our studies focus mostly on silicate glasses, the following
description will be about SiO2 network. However, there are some studies
about other glass compositions such as phosphate glasses [84], borosilicate
glasses [85], and germanate glasses [86]. In the vicinity of crack tip, the
silica network can be deformed. This deformation mainly impacts Si-O-Si
inter-tetrahedral bond angle (The O-Si-O tetrahedral bond angle will also be
a�ected, but to a much lesser extent). Hence the polar moment of Si-O bond
will be modi�ed through deformation and this is very important in term of
energy that is required for H2O molecules to approach Si-O-Si bonds [87�89].
Michalske et al. [87] proposed a three step mechanism for the hydrolysis of
silica network:
1. The glass surface adsorbs the water molecule
2. Two hydrogen bonds are created, one between the silicon atom be-
longing to the Si-O-Si bridge and the oxygen atom from the water
molecule, and the other between the oxygen atom belonging to the
siloxane bridge and the hydrogen atom from the water molecule
3. The Si-O bond is broken, and two silanols (-Si-OH function) are cre-
ated.
SiO2 +H2O ↔ 2Si+OH. (2.1)
It was revealed that a decrease in the inter-tetrahedral angle (Si-O-Si),
coupled with a slight decrease in the tetrahedral angle O-Si-O, results in a
tremendous increase in the reaction rate. It should be mentioned that it is
not the increase in the Si-O-Si bond angle that causes the lowering of the
total energy barrier for hydrolysis to occur, but instead it is a decrease in
this bond angle that may occur through a local pinching of the glass network
2.3. Parameters a�ecting deformation regimes 21
that may exist locally within edge-sharing structures or resulting from the
deformation of the 3-D glass network as a consequence of the high strain
gradient that exists in the vicinity of a loaded crack tip. An increase in
the dissolution rate of the silica and soda-lime silica glass was seen for the
densi�ed glass in indentation experiments [90].
The humidity can in�uence the appearance of types of cracks as well.
While there is almost a total lack of radial cracks at 0% humidity, the lateral
cracks, which never reach the surface, extend over a large distance in soda-
lime silica glass. However, Sub-surface lateral cracks, formed just behind
the indenter, were found to be insensitive to the hygrometric rate and to
remain under the surface of the material [1]. Furthermore, large chips can be
observed at 30% relative humidity. In contrast, the grinding regime is barely
reached at 3 N in a humid environment, whereas at 1 N it is well developed for
dry conditions. Both friction coe�cient and subcritical crack growth, which
are humidity-dependent, do play a major role here [54]. The humidity has
been reported to decrease the strength of glass as well. Proctor et. al. [91]
explained that the strength of silica degraded by increasing the humidity of
environment and this was attributed to the rate of reaction of water molecules
at the stressed crack tip, the mobility of water molecules toward the crack
tip and the availability of water molecules. The humidity causes on one side
the transition between di�erent regimes to develop earlier in the scratching
experiments and on the other side increases the crack velocity [1, 15, 92, 93].
If the crack size is reduced su�ciently, the water can always di�use to the
crack tip at a rate su�cient to provide a stress corrosion environment.
Doing indentation experiments in other environments like bu�er solutions
has also been reported. Mould found that the strength of soda-lime glass
was relatively insensitive to bu�er solutions ranging in pH from ∼1 to 13.
He found that the strength increased for pH values greater than 13 and
decreased for pH less than 1 [80, 94]. In summary, it can be said that the
water in glass is known to decrease the mean connectivity of the network,
thus leading to a decrease in properties such as Young'modulus and viscosity
as its content rises [95].
22 State of the art
2.4 Compositional dependence of deformation in
glass
As with most materials, the mechanism of inelastic deformation of glasses is
closely linked to their structure. When exposed to local mechanical contact
glass surfaces undergo permanent microscopic deformation reactions [41,80].
The type and extent of these reactions is strongly composition-dependent and
have been studied by various researchers [96�99]. It is now widely accepted
that in �free volume�regions, where mechanical coupling to the surroundings
is weak, inelastic relaxations become possible by local atom rearrangements
or molecular segment rotations without signi�cantly a�ecting the surround-
ings [80].
Using normal indentation experiments, a general distinction has been
made between �normal�and �anomalous�glasses according to the presence of
shear �ow and structural compaction, respectively [100�102]. It was found
that the degree of possible structural compaction correlates with the atomic
packing density and the Poisson's ratio of any given glass composition, pro-
viding parameters and a guideline for dedicated chemical tailoring [103].
Based on this understanding, less brittle glasses have been discovered [104]
which o�er increased defect resistance. A large number of studies have been
following this route [105]. Lawn and Marshall [106] introduced a brittleness
parameter B, that accounts for two competitive processes, plastic deforma-
tion and crack propagation and it is calculated as:
B = H/Kc (2.2)
Where Kc is the fracture toughness and H is the Meyer's hardness. The
higher the B, the more brittle is a material and from here it is possible to
compare the brittleness of the glasses of the same family.
The contributions of shear �ow and structural compaction to the over-
all of permanent deformation can be quanti�ed through classical relaxation
experiments [107]: using a normal indentation test, volume and topography
of the residual imprint are compared to those of the same imprint after ex-
posure to a temperature around Tg for prolonged time [108,109]. Assuming
full recovery of structural compaction as a result of thermal relaxation, the
degree of compaction is then obtained from the volume di�erence while the
2.4. Compositional dependence of deformation in glass 23
residual is related to shear �ow. Studies of this type have been conducted
on a variety of glass types, e.g., Refs. [108�112].
Here, coordination number evolution can play a role too. Fused silica
and window glass start to permanently densify above 10 GPa, then reach a
saturation level above a pressure of 20 GPa, whereas silica has a saturation
level of permanent densi�cation ratio of 21%. Soda-lime silica glass, such as
a window glass, saturates at a 6.5% densi�cation ratio (Fig. 2.2).
Figure 2.2: Maximum density relative variation after high hydrostatic pres-
sure testing at room temperature as a function of poisson's ratio. The atomic
packing density Cg for some compositions is also given [103]. Reprinted
from [15]
This saturation level was shown to be linked in some way to the Poisson's
ratio of the glass [103, 113, 114] and Poisson's ratio is correlated to atomic
packing density, Cg. Cg is de�ned as proportion of minimum theoretical
volume occupied by the atoms to the corresponding e�ective volume of glass.
The glasses with low atomic packing density deform mostly by densi�-
cation mechanism and the ones with closed pack systems go mostly through
shear deformation mechanism. In general, the densi�cation process is asso-
ciated with a signi�cant decrease of the intertetrahedral angle, for example
24 State of the art
Ge-Se-Ge in chalcogenide glass GeSe4 and Si-O-Si angles in SiO2 glass. This
can be due to small or undetectable changes of the interatomic distances
(adjacent neighbors), and a gradual increase of the average atomic coordi-
nation (from 4 to 6 in amorphous silica, from 3 to 4 in B2O3 glass, from
fourfold to sixfold for Ge and from twofold to fourfold for Se in GexSe1-xglasses) [101,115].
The transition from normal to anomalous behaviour by adding sodium
and calcium oxides to SiO2 was shown clearly by Limbach and his col-
leagues [112]. For anomalous glasses such as silica, glass deforms essentially
by densi�cation, while in normal glasses the plasticity composed of shear
�ow [100]. Le Houérou and his colleagues showed that the scratchability is
greatly a�ected by composition moving from silica toward di�erent composi-
tions of soda-lime-silica (SLS) glasses. For example, in ramp load scratching
experiments, the microabrasive regime appears in low-load domain for fused
silica and SLS glasses with low silica contents, whereas the lateral chipping
happens for samples with higher amount of silica. Higher amount of silica
leads to earlier appearance of microabrasive regime, except for fused silica
which has an anomalous behaviour.
In summary, it seems that glasses from the devitrite phase �eld that
include crystal nucleations, are sensitive to chipping and glasses with silica-
like networks appear to be much more resistant to both crack propagation
and chipping during scratch experiments. At atomic or molecular scale,
the glasses with high silica content have a better resistance to chipping and
micro-cracking and that is due to the open structure of these glasses network
that allows for both network �exibility and �ow-densi�cation [1, 15,97].
2.5 Contribution of friction to materials behaviour
in indentation experiments
Although there are fair number of studies on the frictional sliding behavior of
various materials such as nanocrystalline ferrite [116], metals and lubricant
oils [117], contact lenses [118], stainless steel sheets [119], graphene [120],
polymers [121�124], aluminum and steel tools [125], the number of such
investigations on glasses under sharp contacts is limited.
2.5. Contribution of friction to materials behaviour in indentationexperiments 25
The friction coe�cient is a critical parameter in designing the mechan-
ical systems with contacting surfaces, modelling of friction-induced vibra-
tions, mechanism of lubrication and where the comfort of soft movements
are needed. However, modelling frictional behaviour is not simple, since
friction force depends on various parameters such as surface roughness, true
contact area, normal load, dynamic behaviour of contact interface with vi-
bration, material transfer, sample thickness, test con�gurations and sliding
systems [4, 119,126�128].
The �rst systematic study of the friction of glass was reported by the
Hardys [129, 130] in 1919, who studied the spreading of �uids on glass [67].
Since then investigations have been carried out to understand the relation-
ship between di�erent parameters such as surface condition, loading, scratch-
ing speed and humidity with friction coe�cient [68]. For instance, a clean
surface without any debris or thin �lms has a high friction coe�cient. The
presence of humidity at the interface results in liquid-mediated adhesion,
which may result in higher friction. It is also being reported that the friction
coe�cient increases as a function of load almost linearly for glass iron, and
aluminum sliding on glass in vacuum and atmosphere saturated with H2O.
However, this behavior is not the same in all conditions. For example, in
the case of glass sliding on glass, the coe�cient of friction remained unaf-
fected by increasing the pressure from 10-10 torr to 1 torr, but from 1 torr
to atmospheric pressure, the coe�cient of friction increased. In term of en-
vironmental conditions, the adhesion force for glass in the presence of water
is more than three times that for glass in the presence of octane [131,132].
Bensaid and his colleagues [68] investigated the relationship between fric-
tion coe�cient and loading for a soda lime silica glass by ramp load scratch-
ing. They introduced a model to calculate the approximate damage loads in
scratching experiments by considering the cracking threshold. In the case of
scratching of the glass, they considered that the tangential e�ort (Ft) should
be divided to a ductile deformation e�ort (Fdef), a coulumbian friction e�ort
(Ff), and a cracking e�ort (Fcr):
Ft = Fdef + Ff + Fcr (2.3)
26 State of the art
and thus,
µ0 =Ft
W=
Fdef + Ff + Fcr
W= µdef + µf + µcr (2.4)
where µdef = tan(β)= constant (considering a pure plastic deformation),
and β is the rake angle, µf =Ff
W = constant (considering a Coulombian
friction).
Assuming Fdef and Ff constant, they considered the apparent friction of
coe�cient to be a result of the cracking e�ort and hence dependent to the
depth of cracking. By setting the depth of crack to zero, a threshold was
found for loads below which there is no median cracks and over which the
transition load for radial/lateral cracking will start. They further found that
the friction coe�cient increases with the increase of the load until a certain
value and then beyond this load it stabilizes. Liu [133] showed that the
friction coe�cient �rst decreases and then increases with increasing normal
load when conical spherical indenter slides over a fused silica glass, while Wei
[134] and Liu [?] revealed that coe�cient of friction has di�erent behaviors
when increasing the load at various scratching velocity on the same material.
One fact is clear: friction coe�cient is not only a function of load, but also
a proper loading range should be chosen to observe any variation of it.
Moreover, the friction of coe�cient is also velocity rate dependent. One
major consequence of �uctuation of friction force or sliding velocity is the
creation of some oscillations that are called �stick-slip�phenomenon. The
term �stick-slip�was coined by Bowden and Leben [135] and can degrade the
materials performance signi�cantly by causing vibrations that lead to cracks
and wear [136]. During the stick phase, the friction force builds up to a
certain value and once a large enough force has been applied to overcome
the static friction force, slip occurs at the interface [44]. The latter phe-
nomenon can be accurately investigated in a variety of controlled conditions
(e.g., loading, scan velocity, and temperature) using atomic force microscopy
(AFM) [137�140].
As an example, it has been recently demonstrated that the formation
of nanoripples on polymers can be understood as a combined e�ect of the
time-increasing shear stress imposed by the slider (i.e., the sharp probing
tip) and the viscoplastic response of the material. In this way, the rippling
2.5. Contribution of friction to materials behaviour in indentationexperiments 27
process appears to be ruled by �ve parameters: normal force, indentation
rate, scan velocity, tip geometry, and lateral contact sti�ness [29,141�143].
Chapter 3
Experimental methodology
3.1 Ramp load scratching
By ramp load scratching the response of material can be studied over a range
of loads in a single test rather than many constant load tests and usually
a transition from elastic to plastic deformation on the surface is observed.
In this test, a tip is brought into contact with the sample, Then the tip is
loaded with a constant loading rate, while simultaneously translating the
sample. Prior to and after the scratch test, a single line scan of the surface
topography is completed for comparing the original surface to the deformed
one. Therefore, each ramp load scratching tests comprises of three steps:
a single-line prescan of the area to be tested, the ramp load scratch test,
and a �nal scan to evaluate the residual deformation [144]. The deforma-
tion regimes induced by ramp load scratching were studied in a commercial
vitreous silica and a metallic glass sample.
3.1.1 Ramp load scratching test on vitreous silica
Instrumented nanoindentation (G200, Agilent) was employed to generate
quantitative data on the scratch resistance of commercial grade vitreous
silica (Heraeus Suprasil 1). The experiment comprises control of the normal
load LN on a Berkovich tip and recording of the lateral load LL during lateral
displacement as illustrated in Fig. 3.1.
29
30 Experimental methodology
Figure 3.1: (a) Schematic of the determination of lateral load LL during
lateral displacement of Berkovich indenter
The value of LL results from a speci�c rate of normal loading and lat-
eral displacement. It is determined from the lateral sti�ness of the indenter,
KL, and its displacement in x- and y-directions, shown schematically in Fig.
3.1. The overall observation length (lateral displacement) was kept constant
among all samples (1.0 mm). Samples themselves were cylindrical with a
diameter of 33 mm and thickness of approximately 3 mm. On the studied
surface, they were sequentially polished with dry silicon carbide powder with
grain sizes of 70, 40 and 9 µm, and �nally with a suspension of diamond pow-
der with a grain size of 1.0 µm, leading to an average roughness of 1.19 µm
(mean arithmetic height, taken from confocal microscopy) and subsequently
stored in vacuum.
Directly before analysis, the samples were cleaned in an ultrasonic bath
of pure isopropanol for 5 min at room temperature, and subsequently �ushed
with ethanol. Tests were conducted by increasing the normal load LN from
0.05 mN to 300 mN during lateral displacement at rates of 10, 50, 100, 150,
300 and 500 µm/s across the overall lateral displacement range of 1.0 mm,
at room temperature. This corresponds to normal loading rates between 3
mN/s and 150 mN/s. The employed tip geometry is shown in Fig. 3.2.
Scanning was conducted in edge forward con�guration (EF, Fig. 3.3).
For each test, an initial specimen surface pro�le was obtained before scratch-
ing by pre-scanning the sample's surface with the indenter under a load of
3.1. Ramp load scratching 31
Figure 3.2: a 3D representation of the employed tip, obtained by wide-�eld
confocal microscopy.
50 µN. While testing, both the penetration depth and the value of LL were
continuously monitored. After scratching, the surface pro�le of the sample
was scanned again under the same conditions as during the pre-scanning
stage. For each loading rate, 20 scratches were performed.
Figure 3.3: The tip con�gurations during scanning, edge-forward (EF, ap-
plied here) and face-forward (FF)
32 Experimental methodology
3.1.2 Scratching of metallic glass by a spherical indenter
Indentations and scratch tests were performed on the surface of Zr55Cu30Al10Ni5metallic glass. The samples were received from France and a thorough de-
scription of sample preparation can be found in ref. [145]: They were pre-
pared using an arc melting method with a mixture of pure Zr, Cu and Al met-
als in an argon atmosphere. By using an arc tilt casting method, cast BMG
cylindrical rod specimens (Φ: 8 mm × L: 60 mm) were obtained [145�147].
A high speed diamond/copper saw was used in order to get 50 mm long sam-
ples. The density, ρ = 6.776 g/cm3 was measured using Archimedes'principle
technique. The Young's modulus E = 85 Gpa and Poisson's ratio ν = 0.370
at room temperature were measured by ultrasonic echography using 10 MHz
piezoelectric transducers in contact with the sample via a coupling gel. E
and ν are expressed as:
E = ρ(3V 2L − 4V 2
T )/((VL/VT )− 12) (3.1)
and
ν = (3V 2L − 4V 2
T )/(2(V2L − V 2
T )− 1) (3.2)
where VL and VT are the longitudinal and transversal wave velocities, re-
spectively. The Tg = 688 K was measured by di�erential scanning calorime-
try (DSC) [148].
In Otto Schott Institute of Materials Research a conical diamond tip (E
= 1141 GPa, Poisson's ratio = 0.07, e�ective tip radius = 4690 nm) was used
to perform indentation imprints at loads of 10, 20, 30, 40, and 50 mN. The
scratching experiments were performed at the same indentation loads and on
the lengths of 100, 200, 300, 400 and 500 µm subsequently. A loading rate
of 1 m/N was chosen for all scratching experiments. After a pre-scanning of
the surface with the load of 50 µN, the experimental load was applied and
in the end of it the scratch was scanned again with a load of 50 µN. Both
lateral load and penetration depths were recorded during this phase. For
each experimental condition, 5 tests were carried out. A scanning electron
microscope from JEOL company (JSM 7001F) was used to investigate the
sample surface after indentations and scratchings.
3.2. Constant low load scratching 33
The surface was further investigated by an atomic force microscope (AFM)
device as well. The measurement were carried out in Leibniz Institute of Pho-
tonic Technology (IPHT) in contact mode using a SNL tip A (Sharp Nitride
Lever) from Bruker. The device was the model Dimension Edge, equipped
with a 100 µm × 100 µm scanner and a maximum z-range of 10 µm. The
AFM data were analysed by WsxM 4.0 [149] software.
3.2 Constant low load scratching
In constant load scratch testing, the normal force is maintained at a con-
stant level while scratching the sample. By this method, the friction can
be measured during scratching [44]. The scratching test at constant load is
performed for a variety of reasons: to characterize material, to determine
the e�ects of variables, and to select the material for a speci�c application.
Two studies were performed in the constant load scratching: one on vitreous
silica and the other on three di�erent silicate glasses.
3.2.1 Scratching at constant load by a Berkovich indenter on
vitreous silica
The scratch tests and AFM imaging were performed on commercial-grade
vitreous silica (Heraues Suprasil 1). A load-controlled nanoindenter (G200,
Agilent) equipped with a Berkovich diamond tip was used to generate surface
scratches. After a pre-scanning phase with a loading force below 50 µN,
the tip was suddenly halted and the load was increased up to the chosen
setpoint (between 10 and 30 mN, i.e., within the elastic-plastic regime [150]).
Scanning was resumed shortly after until the desired scratch length was
reached. At this point, the tip was again halted, and the loading force
brought back to the prescan value. Together with the penetration depth,
the lateral force was recorded during the whole process.
The resulting scratch grooves were subsequently imaged using AFM (Nano
Wizard 4, JPK Instruments) in contact mode in the group of professor Enrico
Gnecco. Silicon nitride probes (Tip B, SNL-10, Bruker) with force constant
of 0.12 N/m and resonance frequency of 23 kHz were used, and the fast scan
direction was oriented along the scratch direction. All images were analysed
using JPK proprietary software and WSxM 4.0 [149].
34 Experimental methodology
3.2.2 Constant low load scratching on silicate glasses
3.2.2.1 Glass samples
Commercial-grade vitreous silica (Suprasil 1, Heraeus), a borosilicate glass
(Boro�oat BF33, Schott), and a standard soda lime silicate glass (Optiwhite,
Marienfeld) were chosen for this study. Compositions of these glasses are
provided in Table 3.1. The silica samples were polished stepwisely on dry
silicon carbide powder with grain sizes of 70 µm, 40 µm and 9 µm. In the
�nal polishing step, a suspension of diamond power with a grain size of 1
µm was used. The other two glass types were used as received. Specimens
of about 30 mm in diameter and 2 mm (silica and soda lime silicate) or 1.1
mm (borosilicate) in height were cut from the glasses and stored in vacuum
between experiments. Directly before indentation studies, the samples were
rinsed with acetone and dried in �owing nitrogen.
3.2.2.2 General characterization
Physical properties of the three glass types are provided in Table 3.1. They
were obtained for this study by instrumented indentation using a nanoin-
denter platform (Agilent G200) and ultrasonic resonance, respectively [151].
Table 3.1: Glass transition temperature Tg, density ρ, Young's modulus E,
shear modulus G, bulk modulus K, atomic packing density Cg and Poission's
ratio ν of the studied glasses.
sample name Silica SLG BF33
Composition SiO2(Suprasil 1)72SiO2.13.9Na2O.8.8CaO.4.3MgO.
0.6Al2O3.0.4K2O.0.2SO3.0.02Fe2O3
81SiO2.13B2O3.4Na2O/K2O.2Al2O3
Tg(0C) 1120 545 525
ρ(g/cm3) 2.203 2.569 2.215
E(GPa) 72.0 71.0 62.3
G(GPa) 31.2 28.8 26.1
K(GPa) 34.6 44.5 33.7
Cg 0.457 0.514 0.475
ν 0.153 0.234 0.192
All indentation and subsequent scratching experiments were performed
in air at 25 0C. Normal indentation was done at constant strain-rate in
the continuous sti�ness measurement (CSM) mode, allowing for continuous
3.2. Constant low load scratching 35
measurement of sti�ness by superimposing a small oscillation on the primary
loading signal and analysing the resulting response of the system. The den-
sities ρ were determined with the Archimedes method at 25 �in ethanol.
From this, the packing density Cg was estimated, [152].
Cg = ρ
∑︁fiVi∑︁fiMi
(3.3)
where Vi = 4/3πN (xrA3 + yrB3) is the theoretical molar volume of the
ions of a generic compound AxBy, Mi denotes the molar mass of the ith
component present in the molar fraction fi, N is the Avogadro number, and
rA and rB are Shannon's ionic radii of the involved ion species (using rO =
135 pm) [153].
3.2.2.3 Scratching and indentation tests
Since literature data on indentation volume recovery by thermal relaxation
exhibit notoriously high scatter [108, 109], we initially conducted original
reference experiments by normal indentation. For comparability with the
subsequent lateral tests, these were done with a 3-sided Berkovich tip (in-
stead of a Vickers tip which is used in most of the literature studies). Lateral
testing was subsequently performed by using the tip in edge-forward con�g-
uration with constant normal loads of 30, 23, and 17 mN on silica, SLG and
BF33, respectively, and two di�erent loading rates for each sample (10 and
50 µm/s). The loads were chosen so as to avoid the occurrence of chipping or
microabrasion. In each scratching experiment, a pre-scan was conducted at
a low loading force of 50 µN. After that, the desired load was applied rapidly
(limited only by the indenter response rate) and kept constant on lines of 35
µm (BF33 and SLG) and 70 µm (silica), respectively. A post-scanning phase
with the same load value as the pre-scan concluded each scratching measure-
ment. All experiments were carried-out at ambient humidity, using the same
tips and shortest possible delay times (<12 h) between each experiment.
3.2.2.4 AFM imaging and subsequent heat treatment
After normal and lateral indentation, the residual indents and the scratch
grooves were imaged by atomic force microscopy (AFM, Nano Wizard 4, JPK
36 Experimental methodology
instruments) in tapping mode in the group of professor Enrico Gnecco. Prior
to that, the samples were again cleaned in an ultrasonic bath of ethanol for
5 min at room temperature, �ushed with acetone and dried properly. Silicon
probes (PPP-NChauD, Nanosensors TM) with a nominal force constant of 42
N/m and a nominal resonance frequency of 330 kHz were used for mapping.
Thermal annealing was conducted in dedicated furnaces with high tem-
perature stability. For SLG and BF33, we used a dilatometer furnace (Net-
zsch) with �ne temperature control and a �at pro�le over a length of <5
mm. The silica sample was relaxed in a bottom lift furnace (Nabertherm
P 310) with an additional thermocouple positioned directly on the sample
for manual control of the local temperature. For all samples, annealing was
done at 0.95Tg, i.e., 511±2 0C for SLG, 498±2 0C for BF33, and 1060±5 0C
for silica (the Tg values were extracted from the data sheets of the glasses;
they are provided in Table 3.1). For SLG and BF33, annealing was done for
1h. For silica, two separate experiments were conducted at 1h and at 2h,
respectively.
AFM images were taken before and after annealing. The time between
images was limited only by the cooling rate of the annealing furnace; it
was <3h for SLG and BF33, and <6h for silica. Through this rapid data
acquisition, secondary relaxation reactions were excluded as far as possible.
Chapter 4
Results and discussions
Scratch-induced surface of Silica under ramp load
scratching
The optical analyses performed on the surface of vitreous silica after ramp
load scratching con�rmed the general phenomenon of sequential plastic de-
formation, chipping and micro-abrasion Fig. 4.1 [7]. Beyond the plastic
regime, the cracks which occur around the scratch groove are mostly surface
chips or lateral cracks.
The types of cracks occurring on the surface are clearly load dependent.
Also the scratch pattern is strongly dependent to the normal load level and
by increasing the load, di�erent regimes of deformation take place that are
schematically shown in Fig. 4.1.
A broad variety of parameters determines this phenomenology, includ-
ing the rate of scratching, the indenter geometry relative to the scratching
direction, the applied normal force, glass surface conditions, environmental
atmosphere and humidity, and the presence of debris or impurities on the
specimen surface, as discussed in section 2.3. So far, the concrete action of
these parameters has received only very limited attention [1, 26, 27]. This is
particularly the case for the technically relevant question of compositional
dependence. Here, recent approaches to compositional development rely
largely on the assumption that data obtained from normal indentation cor-
relate directly (or even linearly) with damage resistance under lateral contact
load. The consensus is that the indentation response of glasses is governed by
37
38 Results and discussions
Figure 4.1: (a) Typical scratch pattern which is observed on silicate glasses
during steady scratching with increasing normal load. (b) Scratch pattern
of vitreous silica observed at ramping load of 0.05-300 mN and scratching
rate of 100 µm/s.
the interplay of elastic deformation, structural compaction and shear [154].
Relaxation studies can subsequently be used to evaluate individual contri-
butions of the latter two [108, 112, 155]. Then, the ability of the considered
material to compact depends directly on its free volume, on molecular scale,
and correlates with Poisson's ratio [103]. Accordingly, vitreous silica, with
exceptionally low Poisson's ratio and high free volume, exhibits a degree of
structural compressibility which beats that of almost all other glasses. How-
ever, it has also become clear that the structural reactions which underlie
damage in�iction are signi�cantly more complex [151].
Although there are some studies investigating the relationship between
materials composition and damage resistance through indentation experi-
ments [108, 109], not much work has been done on the role of densi�cation
and shear �ow in lateral indentations. This was the motivation to study the
role of densi�cation and shear �ow in low load scratching regime (plastic
regime region in Fig. 4.1) on two anomalous and one normal glass. Addi-
tionally, some wavy patterns that appear in this region were investigated by
4.1. Studies at low load scratching in plastic regime of deformation 39
AFM. The results are presented in sections 4.1. By increasing the load in
lateral indentation, other deformation regimes take place, as mentioned and
shown in Fig. 4.1. From here, two studies were performed in higher loads on
vitreous silica and a metallic glass and the results are presented in section
4.2.
4.1 Studies at low load scratching in plastic regime
of deformation
As described in previous section, the initial ramp load scratching experiment
performed on the surface of vitreous silica provided valuable information
about di�erent deformation regimes taking place within the groove. From
here, four di�erent studies were designed that focus on low load and higher
loads (ramp load) scratching to determine some tribological properties of
three oxide and one metallic glass. Two studies which were performed in
constant low load scratching in the section of plastic regime deformation are
explained further in the next two sections (4.1.1 and 4.1.2).
4.1.1 Relaxation of scratch-induced surface deformation in
silicate glasses
In this study, the contributions of shear �ow and structural compaction to
the overall of permanent deformation was quanti�ed through classical relax-
ation experiments within the plastic regimes of silica, borosilicate and soda
lime silicate glasses. By using normal and indentation test, volume and to-
pography of the residual imprints are compared to those of the same imprint
after exposure to a temperature around Tg for prolonged time. Yoshida's
protocol of deformation volume analysis is adopted [108,109] before and af-
ter thermal treatment in order to reveal the roles of compaction and shear
�ow in comparison to normal indentation.
Data analysis The AFM images were �rst �attened using the WsxM
software [149] to exclude the slope of the untreated substrate from the anal-
ysis. The same software was used to measure the indentation volumes and
to extract the scratch groove cross-section pro�les. An exemplary image of
a typical scratch groove (BF33, after relaxation) is provided in Fig. 4.2.
40 Results and discussions
Figure 4.2: Typical AFM micrograph of a scratch groove as used for volume
analysis (here: sample BF33, scratching at normal load FN = 23 mN, 50
µm/s, after annealing for 1h at 498±2 0C).
For each scratch, the average of 10 cross-sections spaced about 2 µm
from each other perpendicular to the scratch direction was used in the fur-
ther analysis. The pile-up and sink-in areas were estimated from the integrals
of the projected cross-sections and multiplied by the length of the consid-
ered scratch section to obtain the corresponding groove volumes. In the
following, V+ and V- will denote the pile-up volume (above the �at surface)
and the sink-in volume (below the �at surface), respectively. Parameters
obtained before and after annealing have the additional subscript �i�(initial)
and �a�(after), respectively. The volume ratios VR of annealing recovery
were calculated following Yoshida et al. [108],
VR =(V −
i − V −a ) + (V +
a − V +i )
V −i
= VR + V +R (4.1)
In the 3D overview AFM image of the scratch groove of BF33 (Fig.
4.2), the pile-up region which formed after 1h of heat treatment can be
clearly seen (all three types of glasses showed some pile-up on the sides of
scratch groove after annealing below Tg). The measured volumes before
and after annealing are presented in Table 4.1 for normal indentation and
scratching. The standard deviation StD stated in the table was calculated
4.1. Studies at low load scratching in plastic regime of deformation 41
for the recovery ratio measured across 10 cross-sections alongside the scratch
groove for each scratch. It is below 10% for all samples.
As already noted, the overall shape of the scratch region is a�ected by
densi�cation (due to structural compaction of the material on molecular
scale) and shear �ow (generating a variation in body shape without a vol-
ume change, most visible in the pile-up zone) [102]. On �rst inspection,
both in scratching and in normal indentation deformation, all glasses exhibit
major but di�ering amounts of densi�cation. Although we used a Berkovich
indenter, this is in general agreement with other observations of the normal
indentation behavior [108,109].
Figure 4.3: AFM top-views and cross-pro�le scans (indicated in the AFM
micrographs) of the residual imprints after Berkovich indentation, before
(left) and after (right) annealing for 1h at 0.95Tg, shown for (a) silica, (b)
BF33, and (c) SLG.
Fig. 4.3 shows AFM top view images of Berkovich indents before and
after annealing for the three silicate glasses. Together with the data provided
in Table 4.1, silica exhibits the highest recovery ratio on normal indentation
(∼ 80%), while the SLG shows the lowest value (∼ 47%). These numbers
42 Results and discussions
Table
4.1:Indentation
andscratch
volumes
before
andafter
annealingfor
di�erent
experim
entalconditions.
Sample
name
Experim
entalconditions
Before
annealingAfter
annealingRecovery
ratioStD
V−i(µm
3)V
+i(µm
3)V
−RStD
V−a(µm
3)V
+a(µm
3)V
+RStD
SilicaScratch
at10
µm/s-1h
18.268.11
4.312.27
0.40.21
Scratchat
50µm/s-1h
17.268.2
3.832.13
0.420.11
Scratchat
10µm/s-2h
20.488.22
0.760.01
4.898.33
0.0090.11
0.770.12
Scratchat
50µm/s-2h
21.274.07
0.780.02
4.735.88
0.080.07
0.780.02
Indent-1h9.31
--
1.65-
-0.83
0.05
7.86-
-1.76
--
0.780.05
7.01-
-1.38
--
0.800.05
Indent-2h2.68
--
1.15-
-0.73
0.05
SLG
Scratchat
10µm/s-1h
7.032.04
0.460.04
3.802.57
0.070.05
0.530.09
Scratchat
50µm/s-1h
6.521.99
0.480.03
3.532.21
0.030.05
0.520.06
indent-1h4.55
2.370.48
0.05
6.213.84
0.380.05
8.043.54
0.560.05
BF33
Scratchat
10µm/s-1h
6.110.51
0.650.009
2.161.31
0.130.009
0.780.01
Scratchat
50µm/s-1h
5.710.53
0.710.006
1.641.38
0.150.02
0.860.02
Indent-1h6.13
1.560.74
0.05
Indent-1h7.12
1.560.77
0.05
4.1. Studies at low load scratching in plastic regime of deformation 43
are consistent with previous reports (Vickers indentation [108,153,156,157]).
The biggest part of recovery stems from the face-to-face distances of residual
indents, as seen in cross-pro�le data in Fig. 4.3.
Silica with the lowest packing density of ions has the highest potential
for compaction under quasi-isostatic load [103]. The pile-up volume which
is observed in the present series of indentation experiments is small in com-
parison to Vickers indentation experiments [108,156]. This is related to the
inherent di�erences in the tip geometry. Small amounts of pile-up indicate
that the major deformation mechanism when using the Berkovich tip is den-
si�cation. Also the volume recovery values for silica and BF33 are relatively
close. This is not surprising considering the fact that both glasses are anoma-
lous [112]. Despite this, the borosilicate glass has a somewhat higher packing
density than silica and a higher number of non-bridging oxygen species, thus,
a slightly lower recovery ratio. SLG on the other hand has the lowest recov-
ery ratio due to its more dense structure, resulting from the presence of a
signi�cant amount of network modifying ions.
AFM top-view images of scratch grooves are presented in Fig. 4.4. Again,
the observed recovery ratio is the highest for silica and the lowest for SLG.
The pile-up volume is considerably smaller than the scratch groove volume,
indicating major densi�cation also in the scratching process. At this point,
we �nd no big di�erence between the overall recovery ratio of scratches and
indents. However, a signi�cantly higher amount of pile-up is observed fol-
lowing scratch deformation. This implies that di�erent deformation modes
are activated in the scratching process as compared to normal indentation,
further con�rmed by notable di�erences in the composition-dependence of
normal hardness and scratch hardness [150]. It is known that the shear de-
formation mode is more pronounced during lateral deformation [8], resulting
in somewhat lower volume recovery after annealing.
The annealing time and deformation-rate dependencies of VR for silica
are indicated in Fig. 4.5(a). The height of the pile-up region increased with
increasing treatment time and the volume recovery ratio almost doubles,
i.e., from approximately 0.4 to 0.8. Within the small variations of scratch
speed we considered here, this observation is independent of the rate of
deformation, Fig. 4.5(b).
44 Results and discussions
Figure 4.4: AFM top-views and cross-pro�le scans (positions indicated in
the AFM micrographs) of the residual scratch grooves after Berkovich edge-
forward scratching, before (left) and after (right) annealing at 0.95Tg, shown
for (a) silica, (b) BF33, and (c) SLG. Annealing times were 1h for BF33 and
SLG, and 2h for silica.
In order to verify the e�ect of stylus geometry on deformation recov-
ery, an additional experiment was conducted on BF33 in face-forward tip
con�guration (due to strong wear on the diamond tips in this set-up, the ex-
periment was not repeated for the other glasses). The resulting cross-pro�le
data are shown in Fig. 4.6. No considerable change of scratch groove volume
before heat treatment was observed for the two di�erent tip con�gurations
when using identical normal loads. However, after 1h of thermal anneal-
ing, the sink-in and pile-up volumes were slightly larger when the tip was in
4.1. Studies at low load scratching in plastic regime of deformation 45
Figure 4.5: (a) Cross-pro�le data of scratches on SiO2 before and after an-
nealing at 0.95Tg for 1 and 2h. (b) Recovery ratio versus annealing time for
di�erent scratch rates.
edge-forward orientation. This results from the reduction of contact surface
when using the sharp apex of tip for scratching as compared to face-forward
orientation. For similar scratch depth, the edge-forward con�guration pro-
duces stronger plastic �ow (analogous to normal indentation with a sharper
indenter). As a consequence, the recovery ratio VR- is smaller than for face-
forward testing. Di�erences in VR+ are a likely result of variations on the
stress distribution, producing a larger compressive zone at the scratch front.
In Fig. 4.7, we compare the volume recovery data of lateral and normal
indentation deformation. On �rst view, we �nd that scratch grooves and
indents have very similar overall recovery values, dependent on glass type. In
order to avoid chipping and microabrasion [158], the present scratch grooves
were generated at much lower normal load (17-30 mN) than the indents
(330-400 mN). However, the scratches experienced additional lateral load
components, approximately ∼ 1/4 of FN for a typical friction coe�cient of
0.25. For weaker loading, there is stronger recovery, in particular VR-, in
very good accordance with normal indentation studies done by Yoshida et
al. [159].
The value of VR- is decreasing with increasing normal load for SLG.
Overall, the highest degree of densi�cation and recovery is found for the
anomalous glasses (silica and BF33). The recovery ratio of the pile-up re-
46 Results and discussions
Figure 4.6: Cross-pro�le scans over a scratch groove on BF33 before and
after 1h annealing at 0.95Tg for face-forward and edge-forward orientation
of the Berkovich tip.
gion VR+ is relatively small for all three types of glasses. As expected, the
experiments carried-out at lower loads resulted in stronger pile-up recovery.
The observed trends in volume recovery and, hence, densi�cation during
scratch deformation exhibit a pronounced correlation with Poisson's ratio.
Also here, the observation is very similar to normal indentation [108]. The
densi�cation contribution to total indentation deformation decreases when
increasing Poisson's ratio from 0.153 for silica to 0.192 for BF33 and further
to 0.234 for SLG. This re�ects the relation between Poisson's ratio and the
atomic packing density [103]. In the anomalous glasses (silica and BF33),
the main mechanism of plastic deformation is densi�cation. Thus, a larger
fraction of the scratch-induced deformation is recovered upon heat treatment.
In the normal glasses (SLG), shear �ow plays a considerable role, re�ecting
in a lower recovery ratio. The network modi�ers may be understood as
providing �easy-slip �paths through a rigid covalent network [43, 160, 161],
leading to enhanced pile-up. Consequently, SLG exhibits pronounced pile-
up generation already during initial deformation, with little further recovery
(VR+). In BF33, pile-up extends during annealing, most probably as a
geometric result of stress relaxation.
4.1. Studies at low load scratching in plastic regime of deformation 47
Figure 4.7: Recovery ratios as a function of (a) loading values and (b) Pois-
son's ratio for all types of glasses. The dark symbols show the values ob-
tained in this study and the red symbols represent the values in the study
by Yoshida et al. [159]. (For interpretation of the references to colour in this
�gure legend, the reader is referred to the web version of this article).
4.1.2 Rippling inside the scratch groove of vitreous silica
During experiments of previous studies, it was noticed that some ripples were
formed inside scratch groove and within the plastic regime of scratching. One
scratch at loading rate of 10 µm representing such phenomenon is shown in
Fig. 4.8.
Since the formation of wavy patterns accompanying the motion of a lo-
calized object sliding on a compliant surface is a basic but not clearly under-
stood phenomenon occurring on very di�erent length scales, studying such
phenomena inside the scratches was motivation of this study. Examples of
this phenomena are the moguls formed in alpine skiing [162], the repeated
impressions left in standard scratch tests on polymers and glasses [163,164],
and the ripples observed when polymer [139], ionic crystal [165], and semi-
48 Results and discussions
Figure 4.8: An atomic force microscopy image of a part of one scratch per-
formed at scratching rate of 10 µm and increasing normal load of 10 mN
showing ripples in the scratch groove.
conductor [166] surfaces are scraped with ultralow normal forces of few tens
of nN.
In this section, an unambiguous evidence and quantitative data on the
occurrence of such regular surface rippling on silica under concentrated loads
of few mN is provided. From the velocity dependence of the ripple repetition
rate, this phenomenon is consistently associated to the stick-slip motion of
the indenter caused by periodic failure of the glass surface and deceleration
of the plowing motion.
The rippling phenomena can be accurately investigated in a variety of
controlled conditions (e.g., loading, scan velocity, and temperature) using
atomic force microscopy (AFM) only [137,138]. As an example, it has been
recently demonstrated that the formation of nanoripples on polymers can be
understood as a combined e�ect of the time-increasing shear stress imposed
by the slider (i.e., the sharp probing tip) and the viscoplastic response of
the material [29]. In this way, the rippling process appears to be ruled by
�ve parameters: normal force FN, indentation rate dz/dt, scan velocity v, tip
geometry, and lateral contact sti�ness k.
If the indentation pit has a Gaussian cross section of half width σ, sur-
rounded by a circular rim of comparable size, stick-slip motion accompanied
by ripples is expected if the inequality FN(dz/dt) > kσv holds, otherwise the
tip will move on continuously. Since the contact area between two solid sur-
faces sliding past each other usually consists of a multitude of tip junctions
which are continuously formed and broken at distinct sites, gaining knowl-
4.1. Studies at low load scratching in plastic regime of deformation 49
edge on regular wear patterns generated by a single tip, not necessarily on
the nanoscale, is crucial for modelling and controlling the response of moving
parts of mechanical components, as well as for fundamental aspects.
In this study, a combination of AFM and nanoindentation techniques is
adopted to investigate the results of stick-slip motion in the early stages of
mechanical contact on the surfaces of inorganic glasses with characteristic
depth and length scales in sub-µm range. Under these conditions, surface
deformation is at the origin of material strength and mechanical failure,
whereby initial �aws act as stress ampli�ers which reduce the applicable
strength by several orders of magnitude [105].
It should be noticed that, while surface scratch tests are routinely per-
formed on glass surfaces, the vast majority of such studies provide only qual-
itative and empirical information on scratch regimes where signi�cant crack-
ing or abrasion occur [63,105], although formation of patterns with repetition
distances of hundreds of µm was also reported in earlier investigations in the
high-loading regime [167]. The elastic-plastic regime, on the other hand, has
been addressed only recently, following major improvements in nanoinden-
tation technology, from the perspective of grinding performance [141, 142],
or scratching hardness [98, 150, 168]. In this regime, the fundamental rela-
tion between stick-slip and topography of the scratch grooves has not been
considered thoroughly so far.
An AFM image of a typical wear scar on the silica glass surface is shown
in Fig. 4.9(a). The scar has a width of about 3.2 µm and a depth of 250
nm. On the upper edge of the scar a modest pile-up of material is observed
with width and height of about 300 nm and 20 nm, respectively.
A cross section across the scratch groove [Fig. 4.9(b)] shows that the
transverse pro�le is not perfectly V shaped. The slope increases continuously
from 7°to 14°when approaching the axis of the groove. Only the limit value is
consistent with the geometry of the Berkovich indenter, which is expected to
cut the specimen with an angle α of about 15°with respect to the horizontal
plane. As shown in appendix (Fig. F1) both width and depth of the scars
increase with the normal force FN, whereas these quantities are not found
to change signi�cantly with the scan velocity v.
50 Results and discussions
Figure 4.9: (a) AFM topography of a silica glass surface previously scratched
(left to right) with a normal force of 30 mN and a scan velocity of 10 µm/s.
Set point: FN = 1.8 mN. (b) Cross section along the light blue line in (a).
(c) Simulated herringbone pattern obtained from the simple repetition of
Berkovich geometry every 350 nm without relaxation e�ects.
The accompanying AFM error signal maps [one of which is shown in Fig.
4.10(a)] clearly reveal the existence of a herringbone pattern across the whole
length and width of the scars.
The constituent ripples are tilted by 62°with respect to the axis of travel,
consistently with the triangular geometry of the Berkovich tip (projected
wedge angle of 120°). Several polishing lines, apparently unrelated to the
herringbone structure, can also be seen. The repetition distance (period)
λ of the ripples is not uniform. The average value of λ can be estimated
from 2D self-correlation of the error signal [Figs. 4.10(b) and 4.10(d)] or,
alternatively, from the 1D fast Fourier transform (FFT) along each horizontal
scan line [Figs. 4.10(c) and 4.10(e)]. The average values of λ coincide, and
FFT allows us to conclude that these values (220 ± 6 nm in the case of Fig.
4.10) are the same on all longitudinal sections (except for the central region
where some impurities are present).
4.1. Studies at low load scratching in plastic regime of deformation 51
Figure 4.10: (a) AFM error signal across the wear scar in Fig. 4.9(a). The
green arrows highlight two polishing lines. Frame size: 10×6 µm2; (b) 2D
self-correlation and (c) 1D-FFT along longitudinal direction extracted from
the region corresponding to the herringbone pattern in (a); (d),(e) cross
sections along the blue lines in (b) and (c), respectively.
As shown in the appendix (Fig. F2) the ripples can be also recognized in
longitudinal sections of magni�ed topography images. Their period is con-
sistent with the estimation in Fig. 4.10. Additionally, their rms amplitude
is 0.81 nm, corresponding to a corrugation on the order of 2 nm. For refer-
ence, ripple occurrence was veri�ed independently by confocal laser scanning
microscopy (Zeiss LSM): see Fig. 4.11.
The scratch test was repeated for six values of v between 10 µm/s and
500 µm/s while keeping FN at 30 mN. Each scratch groove was imaged at
di�erent (nonoverlapping) locations and the average period λ was calculated
as described before. As shown in Fig. 4.12, λ is found to increase almost
linearly with v. From linear regression it is possible to estimate that λ =
λ0 + t0v, with λ0 = (207 ± 8) nm and t0 = (1.07 ± 0.15) ms. This means
52 Results and discussions
Figure 4.11: Laser scanning microscopy image of a wear groove obtained in
the same conditions of Fig. 4.9(a). Scale bar of top view: 20 µm
that the period increases consistently across the range of applied velocities.
The corresponding increase of the rms roughness is more irregular- it varies
within 0.6 nm and 2.2 nm.
Additional information was obtained from the time variation of the in-
dentation depth and lateral pro�les acquired in-situ while the nanoindenter
was scratching the glass surface. As shown in Fig. 4.13(a) the average depth
of the wear groove was z0 = 460 nm, well above the value measured by AFM.
Together with the observation that the cross section is not V shaped, we
can con�rm that the glass signi�cantly recovered during unloading, in line
with previous indentation measurements (without scratching) based on Vick-
ers tips [169]. This behavior, which is not observed in other common glasses
such as soda-lime silicates, can be attributed to the very open structure of
silica glass and the strength of Si-O-Si bonds, facilitating elastic recovery.
From the value of the average lateral force FL = (4.40 ± 0.05) mN during
scratching [Fig. 4.13(b)] a coe�cient of friction µ = 0.15 is estimated. The
value changes only slightly when the velocity is increased (z0 = 475 nm
and FL = 4.5 mN at the maximum value of v = 500 µm/s). Noteworthy,
the corresponding in-situ rms value of the indentation depth, 0.87 nm, is
only slightly larger than the rms value of the ripples pro�les after scratching
4.1. Studies at low load scratching in plastic regime of deformation 53
Figure 4.12: Velocity dependence of the ripples period as measured by AFM
ex situ after scratching with a normal force FN = 30 mN (blue dots) and
linear �t of the experimental data points (red curve).
(0.81 nm), and the rms value of the lateral force ∆FL = 0.06 mN recorded
on line. Regular variations of these quantities corresponding to the period
of the ripple pattern cannot be distinguished with the lateral resolution of
the available setup (100 nm).
Important for the discussion, the indentation depth increases asymptot-
ically when the normal load is applied [as estimated from the red curve in
Fig. 4.13(a)]. The penetration rate dz/dt is indeed found to change from 175
nm/s [corresponding to the black arrow in Fig. 4.13(a)] to 50 nm/s (blue
arrow), with a characteristic time of 4.3 s. When scanning is resumed (at
the point shown by the green arrow) the penetration rate abruptly increases
to 250 nm/s for a short time of about 0.2 s. This means that the pressure
exerted by the nanoindenter is not balanced by the modi�ed surface pro�le,
and the latter is still evolving when the scratching process begins. Addi-
tionally, the lateral force is found to increase continuously when the scan is
resumed, as shown by the curve in Fig. 4.13(b). From the slope of the initial
part of this curve an e�ective lateral sti�ness k = 2.8 kN/m is estimated.
The saturation value of FL = 4.40 is reached quickly, within a time frame of
0.2 s.
54 Results and discussions
Figure 4.13: (a) Time variation of the indentation depth while scratching
with v = 10 µm/s. Scanning was stopped at the time t = 46 s (when the
normal load of 30 mN was applied, black arrow) and resumed at t = 51 s
(blue arrow). A steady state is reached slightly after (green arrow). The red
curve is an exponential �t of the data points in this time frame. (b) Lateral
force vs. indenter position when the scratching process initiates (at x = 20
µm). The positions indicated by the blue and green arrows correspond to
the times in (a).
With the information provided by the combined nanoindenter and AFM
measurements, it is possible to build up a reasonable interpretation for the
surface rippling phenomenon so observed. The time spent by the Berkovich
tip in each dip of the herringbone pattern is easily estimated as λ/v = 22.0
ms. During this time, the tip penetrates the surface by an additional depth
△z = (dz/dt)(λ/v) = 5.5 nm at most. This is larger than the corrugation
of the ripple pattern, as measured by AFM, which again suggests elastic re-
covery (with possible relaxation e�ects). Assuming that the tip apex sticks
to an indentation site while the tip is pulled along the x direction with in-
creasing lateral force FL, a point is eventually reached at which the glass
is not able to resist this force and the tip suddenly slips laterally. With a
cross-sectional area A of the wear groove of 0.74 µm2 [as estimated from the
scan width in the AFM images and the indentation depth in Fig. 4.13(a)]
and the lateral force value of FL = 4.4 mN measured in Fig. 4.13(b), the
corresponding hardness FL/A = 5.9 GPa, in line with recent observations
of the lateral hardness of silica [150]. The average energy dissipated in a
slip event can be also estimated as Ediss = FLλ = 0.97 nJ. This value cor-
4.1. Studies at low load scratching in plastic regime of deformation 55
responds to breaking of only 6% of chemical bonds in the removed volume
Vslip = Aλ = 0.163 µm3 (assuming a density ρ = 2650 kg/µ3 and an av-
erage bond energy of 621.7 kJ/mol [170]), suggesting that the ripples are
associated to nanofracture processes and not to glass �uidization caused by
local heating (which has been reported on larger scales in the context of laser
chemical vapor deposition [171]). Interestingly, for regular scratching within
the elastic-plastic domain, it has been also reported that the work of defor-
mation which is required for the creation of the permanent scratch groove
reaches about one tenth of the corresponding volume energy of silica [150].
To answer the question on what determines the distance travelled by the
tip before it stops again, i.e., the ripple period λ, two di�erent assumptions,
at least, can be made. At increasing velocities, the tip is expected to indent
less deeply the glass surface, reducing the lateral force required to induce the
slip. However, one would expect lower values of λ in this case, as observed on
polymer surface ripples slightly scraped by AFM [29], but in clear contrast
with the results in Fig. 4.12. This di�erence is due to the fact that the
indenter penetrates the surface much more deeply in the present case, and,
as proven by Fig. 4.13(a), it does not retract much more than 2 nm in the slip
phase. The duration tslip of the latter may also not be negligible, as compared
to the stick phase duration, tstick. As proven below, this leads to a linear
increase of λ with v. To this end let us consider the mechanical response
of a rigid object with mass m pulled by a spring with sti�ness k along a
surface. The sliding is slowed down by a constant kinetic friction force Fk
(which, in contrast to more complex numeric models of velocity-controlled
stick-slip [172], is simply assumed to be constant) and it becomes possible
only if the spring force overcomes a threshold value Fs > Fk, corresponding
to the static friction force. Under these general assumptions, it can be proven
(see appendix) that the two phases last for a time
tslip =2
ω0arctan(
vcv), and tstick =
2vcω0v
(4.2)
56 Results and discussions
Respectively, where ω0 =√︁k/m is the resonance frequency of the system
and υc = ω0(Fs-Fk). If v ≪ vc then tslip ≈ π/ω0 and the repetition distance
of stick-slip motion is λ = v (tstick + tslip)= λ0 + t0v, where
λ0 =2(Fs − Fk)
k, and t0 =
π
ω0(4.3)
This linear response (with initial o�set) perfectly matches the experi-
mental results in Fig. 4.12, after noticing that, in steady conditions, λ is
the same as the ripple period. With the values of λ0 and t0 from Fig. 4.12,
and k from Fig. 4.13(b), it is also possible to estimate values of 0.7g for
the e�ective mass m of the indenter and 0.28 mN for the di�erence ∆F =
Fs-Fk. The orders of magnitude of both values are consistent with the mass
of the stylus terminated by the Berkovich tip and the rms value of FL while
scratching (0.05 mN, comparable to the peak value for a perfect triangular
wave). While it is di�cult to draw more conclusions on the e�ective mass m
(depending on the nanoindenter design), the discrepancy in the values of ∆F
may indicate a smoothing of the transition between stick and slip phases,
reducing the lateral force (see Ref. [165] for the observation of this e�ect in
atomic-scale stick-slip measurements). This is also suggested by the blunt
features in the herringbone pattern, which, in Fig. 4.9(c), are compared with
the sharper pattern that would result from the simple geometric repetition
of the Berkovich pro�le every 350 nm. In this context it is also interesting to
observe that the very end of the scratch, when seen from above, also appears
rounded, as showed in the appendix (Fig. F4). This is a further con�rmation
of partial surface recovery after scratching.
4.2 Studies at ramp load scratching in plastic regime
of deformation
The focus of the studies in section 4.2 has been to look more deeply into dif-
ferent aspects of deformation within the constant low load scratching regime
of silicate glasses. From role of densi�cation and shear �ow in lateral inden-
tations to rippling phenomenon within the scratch groove were discussed.
However, it was seen in the Fig. 4.1 that in higher scratching loads other
regimes of deformation take place. Hence, ramp load scratching can provide
worthy information not only in higher loads of scratching, but also during
4.2. Studies at ramp load scratching in plastic regime of deformation 57
transition from elastic to plastic regime on the surface. Such experiments
have been mostly limited to soda-lime silicate glasses [1, 7, 8]. The next
two studies report deformation behaviour of vitreous silica in a quantita-
tive aspect and one metallic glass when applying higher loads in ramp load
scratching experiments.
4.2.1 Statistical analysis of microabrasion onset in vitreous
silica
It is well known that the structural reactions which underlie damage in�iction
are signi�cantly complex [151]. Di�erent regimes occurring during scratching
experiments have been studied in the last years [1,7]. However, a quantitative
study which shows the e�ect of di�erent parameters such as load, scratching
velocity, indenter geometry and so on on the deformation behaviour of glasses
was mostly missing and hence this study was designed.
This investigation focuses on lateral force analyses during scratching of
vitreous silica in an e�ort to obtain increasingly quantitative information
on the scratch resistance of vitreous silica. For this, the e�ect of scratching
velocity (loading rate) on the onset of micro-cracking and chipping is stud-
ied. The correlation of in-situ recordings of friction forces with post mortem
imaging of the scratch enables the identi�cation of onset points for scratch-
induced fracture events and microabrasion. This is subsequently evaluated
through Weibull statistics.
Data analysis
The apparent coe�cient of friction, µ, is approximated from the ratio of
lateral and normal load,
µ =LL
LN(4.4)
This assumes a fully plastic contact in which the progressing indenter is
opposed by the resistance of the material to be removed in its wake (Fig.
4.14).
As a quantitative measure of scratch resistance, the occurrence of the �rst
instantaneous cracking event during scratching was analysed. This analysis
58 Results and discussions
Figure 4.14: Evolution of lateral force during scratching (lateral displace-
ment) while increasing the normal load from 0.05 mN to 300 mN at a scratch-
ing velocity of 500 µm/s. The �rst 200 µm of lateral displacement correspond
to the pre-scan area (in which a normal load of 50 µN is applied). The crack-
ing region is highlighted: arrows mark individual cracking (chipping) events;
the onset of microabrasion is marked with a dashed line.
was performed on recordings of lateral force and apparent friction coe�cient
versus lateral displacement and indentation depth, respectively. In a typical
such scan (Fig. 4.14 or 4.15(a)), an approximately steady or, in the case of
LL analysis, even linear increase is observed in both parameters with increas-
ing normal load during scratching. At a certain stage, this steady evolution
is interrupted by sharp pop-ins. These are assigned to fracture events, lead-
ing to sudden bursts at the progressing scratch tip. As illustrated in Fig.
4.14, the occurrence of these bursts correlates with the post mortem scratch
pattern, where the onset of microabrasion corresponds to the onset of strong
discontinuity in the plot of friction coe�cient versus lateral displacement.
The corresponding value of LL was then obtained by extrapolation of the
initial regime of the plot (plastic regime, Fig. 4.15(a)) across those pop-ins
and taken as the lateral onset load for microabrasion. Besides the onset of
microabrasion, further features can be detected in the data shown in Fig.
4.15(a-b). For one, there is the onset of chipping where there appears to
be a deviation between the in-situ observation of friction (or lateral load)
and the post mortem consideration of the scratch pattern. This indicates
4.2. Studies at ramp load scratching in plastic regime of deformation 59
Figure 4.15: (a) Scratch pattern for fused silica at a scratching rate of 50
µm/s and a normal load which increases from zero to 300 mN, using an
irregular diamond edge for scratching. (b) is a representation of the corre-
sponding variation in the apparent friction coe�cient.
that similar to normal indentation, the initial radial (chevron) cracks appear
during unloading, i.e., after the scratching tip has passed the speci�c point
of occurrence. Such cracking events can therefore not be detected in-situ,
although they may cause weaker artifact features on the subsequent plot of
LL. The concrete veri�cation of the onset point of microabrasion was done
based on the appearance of pop-ins in the in-situ chart as in the example of
Fig. 4.14, and with the help of microscopic images as in Fig. 4.15(a). In all
three methods, an error bar of 5± µm was applied on the obtained value of
characteristic displacement.
Data on the onset of microabrasion were analysed in the form of a Weibull
distribution so as to obtain statistical information on the scratch-induced
cracking behavior of the material. The Weibull distribution is the most
widely used distribution to explain the distribution of �aws in brittle ma-
terials. This distribution not only provides a simple graphical solution, but
it is also useful when there are inadequencies in the data. For example, the
technique works with small samples and it is possible to identify the mixtures
of failures, classes and modes, which was one of the subjects of this study.
60 Results and discussions
The Weibull analysis is based on the weakest link theory according to
which the fracture behavior of a material is linked to the most signi�cant
defect within the material. That means that the �aw that most concentrates
the applied stress causes failure. To make this connection, it is necessary to
assume that fracture results from propagation of a �aw that is an extreme
in a distribution of �aws. These �aws have some distribution function in
relation to stress. The cumulative Weibull probability function is
Pf = 1− exp
[︃−(
σ − σuσθ
)
]︃m(4.5)
where Pf is the probability of failure at or below a given stress σ, σu is a
threshold parameter which represents the minimum stress below which a test
specimen will not break, σθ is the scaling parameter, taken as the character-
istic strength and dependent on specimen size and experiment con�guration,
and m is the Weibull modulus and determines which number of the family
of Weibull failure distributions best �ts or describes the data. Setting σu to
zero and taking the double logarithm of the resulting two-parameter Weibull
distribution yields
ln
[︃ln
(︃1
1− Pf
)︃]︃= m lnσ −m lnσθ (4.6)
The probability value of Pf is obtained through Benard's median rank
approximation,
Pf =i− 0.3
n+ 4(4.7)
where i is the rank of each data point in order of ascending LL and n is the
total number of scratches per experiment. Median ranks are used to obtain
an estimate of unreliability of each failure. It is the value that probability
of failure Pf should have after ith failure out of a sample of n components,
at a 50% con�dence level. 50% is the best estimate for unreliability and this
means that half the time the true value will be greater than 50% con�dence
estimate and in the other half the true value will be smaller than the estimate
[56,173�175]. After linearizing Eq. 4.6, m is obtained from the slope and σθ
from the intercept.
4.2. Studies at ramp load scratching in plastic regime of deformation 61
Phenomenology
In the following, the onset of microabrasion was studied by optical analysis
and the general phenomenon of sequential plastic deformation, chipping and
micro-abrasion were con�rmed, as in Fig. 4.1. In the given example in Fig.
4.15, the onset of microabrasion is clearly visible at a scratch length of ∼450µm. In the plot of µ versus displacement (Fig. 4.15(b)), this corresponds
to the onset of frequent pop-ins without recovering continuous friction. The
overlap between in-situ variations in µ and post mortem optical inspection,
for the microabrasive regime, has two consequences. For one, it indicates
suitability of the observation of µ for accurately quantifying the onset of
microabrasion. Secondly, it indicates that the pop-ins which are observed in
the microabrasive regime correspond to practically instantaneous cracking.
For broader veri�cation, the characteristic onsets of microabrasion (OM)
of all experiments from the present study such as obtained from µ and from
optical inspection, respectively, are plotted against each other in Fig. 4.16.
As an example, there is good accordance between the two ways of observ-
ing OM, i.e., a linear correlation with slope ∼ 1.014 and Pearson product-
moment correlation R ∼ 0.8717 for the chart of Fig. 4.16a (the low value of
R is a result of two individual extreme outliers).
More detailed inspection of Fig. 4.15(b) reveals the occurrence of indi-
vidual pop-ins already before microabrasion, i.e., in the region of chipping.
Here, the points of occurrence do not clearly correspond to post mortem
optical observations. Assuming that these individual pop-ins are not experi-
mental artifacts, this means that the underlying cracks are either too small to
be visually resolved, or that they do not occur on the surface instantaneously,
e.g., that they form sub-surface and/or during unloading in the wake of the
scratching indenter, so that the crack intersection with the scratch groove
which as identi�ed post morten does not correspond to the point of in-situ
observation of the disturbance of the moving indenter. The latter interpreta-
tion is supported by the corresponding observation that certain cracks which
are visible post mortem do not have a parallel pop-in event in the in-situ
scans. In the correlation graphs of Fig. 4.16, such events are the primary
reason for the extreme outliers. Direct inspection of in-situ recordings of
lateral force LL provides a very similar picture (Fig. 4.14). Here as well, in-
62 Results and discussions
Figure 4.16: Determination of the onset of microabrasion (scratch length in
µm) OM through di�erent methods: (a) Post mortem optical microscopy
and in situ observation of the apparent coe�cient of friction, and (b) optical
microscopy and in situ observation of the lateral force. In (c) the determi-
nation of lateral force is considered, i.e., as read directly during in situ scans
and as determined from the length at which OM was observed through the
apparent coe�cient of friction, µ, according to (a). The lines represent linear
correlation �ts with indicated slope and Pearson product-moment correlation
R. Data derive from 20 individual experiments for each of the 6 scratching
velocities. In (c), the three data points marked with an asterix were ex-
cluded from the linear �t. All lines represent linear �ts of the data, with
�tting parameters given in the respective panel.
dividual pop-ins are detected across the phenomenological regions of radial
cracking and chipping (Fig. 4.1).
The occurrence of the �rst pop-in correlates roughly with the transition
from the plastic regime to the regime of radial cracking at a displacement
of ∼ 400 µm (including the pre-scan of 200 µm, Fig. 4.15(a-b) and Fig.
4.14). The non-linear onset of µ in the �rst 200 µm of the scratch is caused
by non-linear LL. Interestingly, the onset of microabrasion corresponds to
the onset of linearity in LL and, consequently, in µ. It remains a question
of further study as to how this non-linearity correlates to, e.g., indentation
size e�ects and the strain-rate dependence of indentation response. Since in
the present experiment, a linear increase of LN is imposed on the system,
information which is provided through in-situ determination of µ or LL is
physically equivalent. Thus, determination of the onset of microabrasion
from scans of µ or LL should provide equivalent results. Individual pop-
4.2. Studies at ramp load scratching in plastic regime of deformation 63
ins are more clearly visible in the LL scan, especially for lower normal load
where they are not smeared-out through mathematical division. Vice versa,
the onset of microabrasion is better seen in the µ scan, which also leads to
better agreement with optical inspection, Fig. 4.16(a-b).
Over a series of experiments with increasing normal load, the scratching
distance and onset load of microabrasion are not constant. As an exam-
ple, such data are provided in Table 4.2 for a scratching speed of 50 µm/s
(corresponding to a normal loading rate of 15 mN/s).
This indicates a strong contribution of the material surface condition
[176] and/or experimental parameters (such as the proper orientation of the
tip in EF con�guration, Fig. 4.14) to the occurrence of scratch-induced sur-
face cracks, similar as with strength testing or determination of the load of
crack initiation through normal micro-indentation [104, 105, 177]. In some
cases, the responsible surface �aws can readily be detected by optical inspec-
tion, e.g., Fig. 4.17.
Figure 4.17: Post mortem optical microscopic image of a scratch generated
at a scratching speed of 10 µm/s under increasing normal load (3 mN/s).
The onset of microabrasion (marked) was observed at a normal load of 153.3
mN and a lateral load of 42.4 mN. In this example, the initiating surface
�aw was a scratch, probably induced during polishing (marked).
Following the above observations, statistical analyses were performed in
order to extract quantitative data on the scratching behavior of vitreous
silica. This included analyses of the probability Pf for the occurrence of
microabrasion. In Fig. 4.18 data are provided for LL at the onset of mi-
64 Results and discussions
Table
4.2:Onset
ofmicroabrasion
(OM)for
aseries
of20
experim
ents,scratching
vitreoussilica
atarate
of50
µm/s
with
normalload
increasingfrom
0.05mNat
arate
of15
mN/s.
Experim
entalerrors
are±5µm
onall
displacement
data,and
±0.01
mNon
allloads.
Displacem
entof
OM
(µm)
experim
entno.
Inspection
ofµ
Optical
inspection
Inspection
ofLL
LNat
OM
(mN)
LLat
OM
(mN)
1193
206273
81.922.1
2275
280266
79.519.9
3158
140190
56.915.7
4643
660499
15054.3
5439
370429
12832.3
6159
105130
38.910.8
7731
746131
39.058.6
8554
334513
15439.2
9111
180128
38.39.5
10779
720703
21155.4
11629
590601
18047.6
12555
593560
16842.7
13430
440431
12932.6
14208
210214
64.115.9
15631
600617
18549.5
16449
500486
14538.2
17550
580540
16243.3
18291
200209
62.616.7
19530
580513
15439.1
20605
525597
17947.1
average446
427.9401.5
162.134.5
4.2. Studies at ramp load scratching in plastic regime of deformation 65
Figure 4.18: Statistical analysis of the onset of microabrasion (OM) in vitre-
ous silica during lateral indentation. Depicted data present the probability
of the occurrence of microabrasion as a function of acting lateral load LL.
They are plotted for varying scratching velocity with gradually increasing
normal load (0.0 mN to 300 mN) as Weibull distribution with the proba-
bility term Pf according to Benard's median rank approximation. OM was
determined from in-situ lateral force measurements. Lines represent linear
�ts of the intermediate failure regime (�t data in Table 4.3). As a guide to
the eye, slopes of 1, 2 and 6 are also indicated.
croabrasion (including the data given in Table 4.2 for the case of scratching
at 50 µm/s, 15 mN/s).
Clearly, the probability of failure is higher at higher lateral loads. A min-
imum value of LL is required to start any abrasion, consistent with obser-
vations [60] on lateral cracking during unloading in quasi-static indentation
experiments. Data on Weibull modulus are summarized in Table 4.3.
Roughly, there are three regimes of failure (failure modes): the �rst fail-
ure mode occurs at relatively low load with relatively high slope (best seen
in the plots for scratching velocities of 10 µm/s and 100 µm/s, Fig. 4.18).
This mode can be attributed to the occurrence of major surface �aws and/or
66 Results and discussions
Table 4.3: Weibull parameters for failure modes I and II and varying speed
of scratching.Velocity (µm/s) m R-value for m
10 1.61 0.973
50 2.73 0.982
100 1.72 0.996
150 2.04 0.974
300 2.82 0.983
500 4.40 0.985
experimental perturbations. In particular, individual outliers at lowest load
indicate the occasional presence of a distinct, single disturbance or �aw.
They are thus not taken into account in the following quantitative evalua-
tion. A second regime is seen at very high load, visible only for high scratch-
ing rates (300-500 µm/s, Fig. 4.18). In this regime, the probability func-
tion levels-o� to an exponential equation, indicating constant rate of failure.
Such independence of mechanical failure on load (random OM) can be in-
terpreted as resulting from high overall surface quality (thus, generally high
abrasion resistance) with very occasional (laterally randomly distributed)
failure-inducing �aws. This means that a high scratching rate smears-out
the occurrence of OM in some speci�c samples with low surface defect den-
sity. Vice versa, it can also be concluded that some �aws are activated only
at low scratching rate: at high enough rate, the indenter is simply passing-by
some types of defects.
For further evaluation, at the moment, only the intermediate regime was
considered as marked in Fig. 4.18. For this regime, the Weibull modulus is
found in the range of roughly 1.6 - 4.4, increasing with increasing scratch
velocity and/or increasing loading rate. Hence, the underlying probability
of failure exhibits a compressed exponential or even Gaussian distribution
which is further compressed with increasing loading rate. Especially at low
scratch velocity, the values are somewhat below but still in the range of those
which are typically found in macroscopic testing of similarly prepared glass
samples, e.g., by ring-on-ring cracking [178]. On the one hand, this signi�es
the much lower tested volume. On the other hand, it also indicates that at
high enough scratching rate (and, thus, tested length), scratch-induced mi-
4.2. Studies at ramp load scratching in plastic regime of deformation 67
crocracking is similarly a�ected by the presence of surface �aws as is macro-
scopic cracking (notwithstanding the above arguments regarding the regime
of high load/high rate).
As noted above, with the exception of the experiment which was con-
ducted at 50 µm/s, the obtained Weibull moduli depend roughly linearly
on scratching velocity. Looking at the exact data (Fig. 4.18), the increase
in the value of m originates from an overall compression of the data. That
is, the underlying probability function is compressed on the low-load side,
leading to postponed activation of certain �aws at higher scratching velocity
and/or accumulation in individual cracking events rather than continuous
microabrasion. Data then catch-up at higher load, leading to a steeper pro-
�le in the Weibull plot. Vice versa, at lower velocity, more time is left for
defect activation and growth. Aside of individual outliers (in the low-load
failure regime, see above), the onset of microabrasion follows a normal or
even compressed exponential distribution. This re�ects a situation where
the proceeding scratch is intersecting randomly distributed surface defects
with a decreasing stress-dependence of their activation to form cracks. A sim-
ilar conclusion was drawn by for the case of soda lime silicate glasses [50,73].
Also for these, it was found that changing the scratching velocity a�ects the
cracking behavior. This was attributed to extended time interval over which
any one surface defect stays in a stressed state at lower scratching velocity,
so that its probability of growing into a visible surface crack increases. It
remains to be examined in future studies how this is related to subcritical
defect growth.
4.2.2 Scratching of metallic glass by a blunt indenter
So far, all the studies of this dissertation were concentrated on silicate glasses.
However, many industrial applications require materials with remarkable and
sometimes contradictory properties. For example, in the �elds of biomate-
rials (dental implants), micromechanics (gears) or in the �eld of jewellery
or watches (luxury watches), materials are needed that are hard, wear resis-
tant, bio-compatible, possess a high yield strength, while being deformable.
Such ideal materials do not exist yet. Metallic glasses have shown a high
potential for industrial applications due to their high strength, high elastic
limits, excellent corrosion resistance, and thermoplastic formability. On the
68 Results and discussions
other words, the combination of their structural and functional properties
make them potential candidates for applications where the use of conven-
tional materials has reached a limit of e�ectiveness. Following these reasons,
investigations on tribological properties of metallic glasses have been the
focus of many studies in the last decades [31�37].
Nonetheless, the dynamic behavior of nanoscratching in metallic glasses
which are relatively new materials in comparison with oxide glasses has not
been given much attention. Ramp load scratching seems an appropriate
method to study the tribological properties of metallic glasses and to col-
lect initial information about the surface resistance of these group of glassy
materials. Such information could likely be used to design constant load
scratching tests later which provide more precise information about the plas-
tic deformation mechanisms of di�erent groups of metallic glasses. Hence,
in this section, some aspects of deformation behavior of a metallic glass
(Zr55Cu30Al10Ni5) which has a good forming ability and a great potential
for industrial applications was studied by ramp load scratching.
These series of experiments were performed with a conical spherical in-
denter. The main goal of scratching experiments with a blunt indenter is to
outline a mechanistic framework for interpreting measurements performed
on elastic/plastic materials. Moreover, at low force levels, the stresses be-
neath a blunt indenter are below the elastic limit, and hence, the tribological
properties of material can be obtained in the absence of plasticity. Moreover,
at higher forces, responses in the transitional elastic/plastic and fully plastic
can also be probed. Selection of the spherical indenter is further motivated
by the recognition that the asperities that make contact during sliding of sur-
faces are more closely represented by protuberances with a constant �nite
curvature rather than ones with in�nitely sharp points [57,179�181].
Fig. 4.19 shows an scanning electron microscopic overview image of two
scratches performed at the maximum loads of 30 mN and scratching rate of
10 µm/s. The scratching direction is from right to left and along this route
the scratch grooves become deeper and wider by increasing the load. At
lower loads the scratch groove is so shallow that it creates a inconspicuous
impression.
Fig. 4.20 shows the load-displacement curve for indentation and scratch-
ing experiments performed at the maximum loads of 20-50 mN.
4.2. Studies at ramp load scratching in plastic regime of deformation 69
Figure 4.19: (a) An Scanning Electron Microscopy overview image of two
scratches performed at load of 30 mN and scratching rate of 10 µm/s. The
whole scratching length is not shown in the image. (b) A pro�le of displace-
ment into surface over the whole lateral length for a scratch at the same
conditions.
In P-h curves for indentations and prior to the �rst pop-in, the loading
curve exhibits a smooth and parabolic shape, which can be described by
Hertz's law for an elastic contact [182]:
P =4
3Er
√Rh3 (4.8)
Where Er is the combined elastic response of the indenter tip and the
glass specimen and h is the displacement into surface. If both contacting
70 Results and discussions
Figure 4.20: The normal load vs. penetratuin depth curves for indentation
(left) and scratching (right) experiments at normal load of 20, 30 and 40 mN.
All scratching experiments were performed at scratching rate of 10 µm/s.
bodies have a curvature, then R in the above equations is their relative radii
given by:
1
R=
1
R1+
1
R2(4.9)
By using a spherical indenter and during the indentation the load-displacement
curve often exhibits a burst of displacements that is called pop-ins and they
can well be seen in the Fig. 4.20. Serrated plastic �ow phenomenon has been
widely observed in BMGs under deformation-constrained loading modes such
as compression [183�192] and especially the �rst pop-in matter. Because
it shows the transition from elastic to plastic behaviour and are believed
4.2. Studies at ramp load scratching in plastic regime of deformation 71
to be the birth of shear bands in nanoindentation experiments on metallic
glasses [32, 189]. By this explanation, it can be noticed in Fig. 4.20 that
the applied load drops at the onset of pop-ins and the �rst pop-in in 4.20(b)
appear at the load of 12.1 mN. There was no pop-in for P-h curves of inden-
tation at the load of 10 mN which means the material showed a rather elastic
behavior. Though at 20 mN load for scratching experiment pop-ins are seen
on the P-h curves (Fig. 4.20(b)), the indentation experiments showed almost
no pop-ins until the load of 40 mN (Fig. 4.20(e)). The P-h curve obtained
at the load of 40 mN for indentation indicates that the deformation at this
load was mostly elastic too. However, around the maximum load, the �rst
pop-ins occurred (Fig. 4.20(e)). The charts of experiments at 50 mN are
not showed here due to the tip blunting and this matter will be discussed
further.
All the pop-in loads for indentation and scratching experiments were
estimated from the P-h charts in Fig. 4.20 and the results are shown in
Table 4.4. The dash lines represent the samples for which it was not possible
to read the pop-in loads clearly. The lateral loads corresponding to these
normal loads were also estimated and shown in the Table 4.4 and excluding
the scratch at 50 mN, they are between 0.13 and 1.6 mN, around one tenth
of the normal loads. The pop-ins appearance is load dependent which is in
agreement with other literatures [193�195]. Lower load activates a smaller
volume of material and such dependence of plastic deformation to sample
size has already been discussed in other literature [196]. Also the higher the
normal load, the higher goes the lateral load. The scattering of pop-in loads
at 50 mN could be related to tip blunting. After all, it is believed that if
the tip blunting would not have happened, we would have had lower pop-in
loads for 50 mN experiment due to higher plastic deformation, as described
before in section 4.1.1.
Fig. 4.21 shows such comparison more distinctively. Another interest-
ing observation is that even for indentations and scratching performed at
identical conditions the onset of plasticity is distributed over relatively large
range. This is in agreement with results of Refs. [32, 197].
For example, loads ranging from 7.84 up to 22.2 mN have been required
to observe the �rst pop-in, in the Cu48Zr48Al4 alloy, although all indentations
were performed under the same experimental conditions. This phenomenon
72 Results and discussions
Table 4.4: Normal loads and lateral loads at which the pop-ins appear for
each experimental load at 20, 30, 40, and 50 mN.
Maximum normal load of experiment (mN) Normal load at pop-in (mN) Lateral load at pop-in (mN)
Scratch at 20 mN 12.1 0.25
- -
- -
17.3 0.13
15.6 0.41
Indent at 30 mN 28.2
-
-
-
-
Scratch at 30 mN 11.9 0.3
12.5 0.19
13.2 0.16
12.5 0.63
- -
Indent at 40 mN 39.9
39.9
38.1
38.4
37.9
36.5
Scratch at 40 mN 19,4 1.6
16.6 1.1
- -
- -
- -
Indent at 50 mN 43.0
43.3
40.4
44.5
39.5
Scratch at 50 mN 33.9 2.44
24.5 2.35
30.0 3.43
23.5 2.55
- -
has at least partly been attributed to the spatial heterogeneity in the local
atomic con�gurations inherent to metallic glasses [197�203]. Yielding can
occur at any stress when the thermal energy is high enough, whereby the
probability for yielding increases exponentially with increasing load [204,
205].
4.2. Studies at ramp load scratching in plastic regime of deformation 73
Figure 4.21: Normal loads at �rst pop-ins appearance for indentations and
scratching (left) and lateral loads for scratching experiments (right).
Schuh and Lund [188] suggested that thermally assisted and stress-biased
yielding always exhibits a spread in yield strength. This is because the ther-
mal noise sometimes favors yielding and sometimes works against it. Yet,
in this case, more experimental data will determine the range more pre-
cisely. Furthermore, the �rst pop-ins in scratching experiments appear at
lower loads in comparison with indentation experiments. It can be con-
cluded that scratching is a more severe deformation mode than indentation
for the same normal load: the in�uence of the tangential load, and therefore
friction among others factors may contribute to the di�erences in the plastic
deformation mechanisms. On the other words, for the same loads, scratch-
ing is more likely able to make the material enter the fully plastic regime of
indentation. Moreover, the higher the load, the higher the number of bands
at the surface, to accommodate plastic deformation [206]. This phenomenon
has been discussed in section 4.2.1 through estimating the probability of
occurrence of a certain type of plastic deformation (in that case onset of mi-
croabrasion) by increasing the load and it was proved that such probability
increases by applying higher load on the sample surface.
It was mentioned that the load-displacement chart of scratching at 50
mN was not shown with other curves due to the tip blunting (the data were
not consistent and it was concluded that something may have occurred here).
The e�ect of normal load on coe�cient of friction (COF) was further studied
74 Results and discussions
to explain the reason. Fig. 4.22 shows the variations of COF along the
scratching distance and it is increasing slightly with the increase of normal
load along the scratch groove and drops in the end of scratch where the
indenter is slowly leaving the surface.
Figure 4.22: Coe�cients of frictions for scratches at loads of 20, 30, 40 and
50 mN. Each experiment was repeated 5 times.
The COFs are also increasing by increase of load from 20 mN to 50 mN.
The increase in Coe�cient of friction (COF) with the applied normal load
both at micro- and macro-scales have already been reported [193�195] and
it could be due to increasing amount of roughening or increase of plastic
deformation at higher loads [33]. The COF close to zero have been due to
the very weak contact between the indenter and surface as a result of low
loads. At the load of 40 mN, the last 3 experiments are showing higher
values than the �rst 2 and it is believed to be related to tip blunting at third
experiment. For the reason of tip blunting, the contact between indenter
and material surface has increased and this indicates an increase in friction
4.2. Studies at ramp load scratching in plastic regime of deformation 75
coe�cient in COF charts. For each load the COF values are closed to each
other for 5 experiments and are between 0 to 0.15 in between the friction
coe�cient estimated by applying load with spherical indenters on the surface
of glasses (fused silica µ < 0.065 at loads of up to 5 N [133], Borosilicate µ <
0.065 for loads between 0 to 6N [207]) and metals (Copper µ <0.25 for loads
up to 1N [4] and for Aluminm 0.4< µ <1 [57]).
In section 4.1.2 it was mentioned that some ripples had been observed
under the microscope that were further studied. In this study, some pat-
tern (semi-circular shape) was also observed inside the scratch groove. The
shapes start to appear in the groove at a certain load and continue to the end
of scratch, as it can be seen in 4.23(a). These patterns were further partly
investigated by Scanning Electron Microscope (SEM) and Atomic Force Mi-
croscope (AFM). Fig. 4.23 demonstrates SEM and AFM images and the
pro�le of patterns along the scratch groove at the load of 30 mN.
In Fig. 4.23(a), it is noticed that these semi-circular shapes have di�erent
frequencies along the scratch groove. Similar patterns have been observed
in some studies carried out on the glasses, however not deeply investigated
so far to authors knowledge [4, 134, 207, 208] and they were described to be
a result of indenter shape on the surface. But so far no study was found on
metallic glasses discussing such patterns. A good e�ort was done to estimate
the wavelengths of these patterns that seem to change with the loading (it
can be seen more obviously in Fig. 4.23). But due to the very shallow depth
of these structures (some tenth of nanometres in comparison with ripples in
section 4.1.2 which had depths in the dimension of hundreds of nanometres),
it was not possible to calculate the precise wavelengths (an example of these
calculations is presented in appendix 5). However, the scratching distance
at which these patterns start to appear was read from SEM images and the
load correlated to this point was determined directly from indenter data and
these were compared with pop-in loads which were estimated from charts of
Fig. 4.21 for the scratching loads of 20 and 30 mN (at the load of 20 mN
only one scratch showed the clear appearance of pattern in SEM images).
Fig. 4.24 shows this comparison.
Interestingly, the pop-in loads and the loads at which the patterns appear
in SEM images are not that far from each other and they are all between 12-
15.5 mN. Even for two di�erent scratching loads, the �rst pop-in is appearing
76 Results and discussions
Figure 4.23: a) An image of a scratch at the load of 30 mN obtained by
Scanning Electron Microscope b) and c) Atomic force microscopy images of
two marked sections of the same scratch in (a), d) and e) Center line pro�les
of AFM images in (c) and (d).
around the same load. From here, we may conclude cautiously that there
could be a relationship between appearance of pop-ins and semi-circular
shapes or in other words, the patterns occurrence is related to formation
of shear bands in material. However, more experiment in di�erent loads is
necessary to con�rm such phenomenon. Another observation is that the pop-
in read from the charts of indenter appear after patterns appearance from
SEM along the scratch length. There is roughly 20-50 µm distance between
pop-ins scratching distance read from indentation charts and SEM data.
The time between appearance of pop-in in indentation data and formation
of patterns on SEM images was estimated to be ∼ 3-5.5 s which is relatively
small considering the total scratching time of <72 s for the load of 20 mN and
<140 s for the load of 30 mN. To answer the question why is this happening
4.2. Studies at ramp load scratching in plastic regime of deformation 77
Figure 4.24: Comparison of pop-in loads read from indenter and the point
of appearance of patterns in SEM images for the scratching loads of 20 and
30 mN. An standard deviation of 5% µm should be taken into account for
the data.
and could it be related to estimation of distances in SEM images or it is
really a phenomena needs more investigations.
Chapter 5
Conclusions
The aim of this thesis was to examine the tribological properties of di�erent
glasses by applying lateral nanoindentation technique. A scratch pattern
produced by ramp load experiment on the surface of silica was the start
point of further studies. This pattern showed di�erent deformation regimes
taking place on the surface at low and high loads. While radial and me-
dian cracks appeared in low load regimes, lateral cracks and microabrasion
were taking place in higher loads. This study showed the potential of more
methodological investigations on various types of glasses. From here, two
study were designed in constant low load and two more in higher ramping
load scratching on more silicate glasses and one metallic glass.
Through relaxation experiments performed on the scratch-induced sur-
face of fused silica(anomalous), borosilicate and soda lime silica (normal)
glasses in low load regime, the role of compaction and shear deformation
was studied. It was demonstrated that structural compaction and shear
�ow occur also in the lateral deformation of a glass surface through scratch-
ing. Applying instrumented indentation with tangential displacement in the
elastic-plastic regime of scratch-deformation, a strong similarity was found
in the volume recovery ratio by post-annealing as compared to normal inden-
tation studies. Silica, borosilicate and soda lime silicate glasses follow the
same trend in terms of compaction recovery with Poisson's ratio as they do
in normal (quasi-isostatic) indentation. Therefore, the same distinction into
normal and anomalous glasses appears to be applicable. On the other hand,
inherent di�erences occur in the absolute presence of deformation modes
79
80 Conclusions
across all three types of glass. In particular, caused by shear deformation at
the apex of the employed Berkovich tip, pronounced material pile-up occurs
in scratching for normal loads which are about one order of magnitude below
reference experiments of normal indentation. This leads to an increase in the
e�ective friction coe�cient and a non-trivial correlation between the scratch
hardness and the normal hardness of glasses.
It was found that lateral indentations with moderate loading forces (up
to 30 mN) on the surface of fused silica form some rippling phenomenon.
This was further studied at di�erent scratching velocities (up to 50 µm3)and
was related to periodic stick-slip motion of the tip. The ripples period was
estimated and showed a rather linear dependency to the scratching velocity.
Since most sliding interfaces of technical interest are ultimately formed by
a multitude of contact points which are abruptly formed and broken, the
information so acquired can be of key interest for understanding much more
complex wear processes occurring on the macroscale. Speci�cally, one could
expect that not only the irregular time variation of the friction force in a
multiasperity sliding contact results from an ensemble of regular stick-slip
events, but the accompanying abrasive wear patterns are ultimately caused
by overlapping (and possible interference) of �ripple-like�features similar to
those reported here in the rather ideal case of an inverted pyramid vs �at
contact. Fourier analysis of the lateral force acquired while scanning may
also help to correlate the time evolution of the stick-slip mechanism to the
topographical features of the resulting surface patterns.
Ramp load scratching was recognized as an appropriate technique to
study the tribological properties of glasses. Since most studies so far focused
on obtaining qualitative information on the surface of glasses, instrumented
nanoindentation with ramp loading was employed for obtaining quantitative
information on the onset of scratch-induced microabrasion on silica glass. For
this, in situ evaluation of lateral force and friction coe�cient was compared
to post mortem optical inspection, following edge-forward scratching with a
Berkovich indenter. Statistical analysis indicated two underlying probability
functions for the occurrence of microabrasion, i.e., the probability for the
propagating scratch to hit a surface �aw and the probability that such an
event causes an observable micro-crack. Dominance of the former follows
an exponential function, re�ecting a purely random distribution with load
independent probability of failure. It was observed only at high scratching
Conclusions 81
velocity after passing a certain normal load. For the latter, the Weibull mod-
ulus was found to increase with increasing scratching velocity, i.e., from ∼ 1.6
to 4.4. Here, low Weibull modulus at low load was attributed to the increas-
ing time of local strain, which leads to a reduction of the load-dependence of
micro-cracking. For silica and employing the present experimental approach,
the critical lateral load for microabrasion (50th percentile) is around 30-40
mN. This value is very probably dependent on extrinsic parameters such as
ambient humidity.
Further, ramp load scratching technique was used to obtain tribological
information on the surface of (Zr55Cu30Al10Ni5) metallic glass which showed
a great potential for industrial applications. Here as well, it was con�rmed
that the scratching is a more severe deformation mode in comparison with
normal indentation. This was argumented through the study of �rst pop-in
P-h charts. The friction coe�cient estimated from indentation data was be-
tween 0 and 0.15, well between the friction coe�cients of glasses and metals.
Further scanning electron microscopy study of the scratches on the surface
showed that there might be a relationship between the start of shear defor-
mation and semi-circular pattern that were observed on the surface.
Zusammenfassung
Das Ziel dieser Arbeit war es, die tribologischen Eigenschaften von ver-
schiedenen Gläsern mit Hilfe der lateralen Nanoindentationstechnik zu unter-
suchen. Ein Kratzmuster Rampenbelastungsexperiment auf der Ober�äche
von Quarzglas erzeugt Ausgangspunkt für weitere Untersuchungen. Dieses
Muster zeigte verschiedene Deformationsregime die auf der Ober�äche bei
niedrigen und hohen Belastungen statt�nden. Während radiale und mediane
Risse bei niedrigen Belastungen auftraten, traten bei höheren Belastungen
laterale Risse und Mikroabrieb auf bei höherer Belastung auf. Diese Studie
zeigte das Potenzial für weitere methodischen Untersuchungen an verschiede-
nen Glastypen. Von hier aus wurden zwei Studie in konstanter niedriger Be-
lastung und zwei weitere in höherer rampenförmiger Lastkratzens an weit-
eren Silikatgläsern und einem metallischen Glas durchgeführt.
Durch Relaxationsexperimente, die an der kratzinduzierten Ober�äche
von Quarzglas (anomal), Borosilikat- und Kalknatrongläsern (normal) Gläsern
im Niedriglastbereich durchgeführt wurden, wurde die Rolle der Verdich-
tung und Scherverformung untersucht. Es wurde gezeigt, dass strukturelle
Verdichtung und Scherung �ieÿen auch bei der lateralen Verformung einer
Glasober�äche durch Kratzen auftreten. Die Anwendung einer instrumen-
tierten Vertiefung mit tangentialer Verschiebung im elastisch-plastischen Regime
der Kratzverformung, wurde eine starke Ähnlichkeit im Volumenrückgewin-
nungsverhältnis durch Nachglühen im Vergleich zu normalen Indentations
Studien. Silikat-, Borosilikat- und Kalknatronsilikatgläser folgen dem gle-
ichen Trend in Bezug auf die Verdichtungserholung mit der Poisson-Zahl, wie
sie es bei normaler (quasi-isostatischer) Eindringung. Daher scheint die gle-
iche Unterscheidung in normale und anomale Gläser anwendbar zu sein. An-
dererseits treten inhärente Di�erenzen im absoluten Vorhandensein von Ver-
formungsmodi bei allen drei Glastypen auf. Insbesondere, verursacht durch
Scherdeformation am der Spitze der eingesetzten Berkovich-Spitze kommt es
zu einer ausgeprägten Materialanhäufung beim Kratzen für normale Belas-
tungen, die etwa eine Gröÿenordnung unter Referenzversuchen der normalen
Eindrückung. Dies führt zu einer Erhöhung des e�ektiven Reibungskoef-
�zienten und zu einer nicht-trivialen Korrelation zwischen der Ritzhärte und
der Normalhärte von Gläsern.
Es wurde festgestellt, dass seitliche Eindrücke mit moderaten Belas-
tungskräften (bis zu 30 mN) auf der Ober�äche von Quarzglas ein gewisses
Ri�elphänomen bilden. Dies wurde bei verschiedenen Kratzgeschwindigkeiten
(bis zu 50 µm/s) weiter untersucht und wurde mit einer periodischen Stick-
Slip-Bewegung der Spitze in Verbindung gebracht. Die Periode der Rif-
felung wurde abgeschätzt und zeigte eine ziemlich lineare Abhängigkeit von
der Kratzgeschwindigkeit. Da die meisten technisch interessanten Gleit-
�ächen letztlich aus eine Vielzahl von Kontaktpunkten gebildet werden, die
abrupt gebildet und gebrochen werden, können die so gewonnenen Informa-
tionen von zentralem Interesse für das Verständnis viel komplexere Ver-
schleiÿprozesse auf der Makroskala. Konkret könnte man erwarten, dass
nicht nur der unregelmäÿige zeitliche Verlauf der Reibungskraft in einem
Gleitkontakt aus einem Ensemble von regelmäÿigen Stick-Slip-Ereignissen re-
sultiert, sondern die begleitenden abrasiven Verschleiÿmuster letztlich durch
Überlagerung (und mögliche Interferenz) von �Rripple-like �-Merkmalen verur-
sacht werden, ähnlich wie die hier für den eher idealen Fall einer umgekehrten
Pyramide vs bei Kontakt. Die Fourier-Analyse der während des Scannens
erfassten Querkraft kann auch helfen, die zeitliche Entwicklung des Stick-
Slip-Mechanismus mit den topographischen Eigenschaften der resultierenden
Ober�ächenmuster zu korrelieren.
Das Rampenbelastungskratzen wurde als geeignete Technik erkannt, um
die tribologischen Eigenschaften von Gläsern zu untersuchen. Da sich die
meisten Studien bisher darauf konzentrierten qualitative Informationen über
die Ober�äche von Gläsern zu erhalten, wurde die instrumentierte Nanoin-
dentation mit Rampenbelastung eingesetzt, um quantitative Informationen
über den Beginn des kratzinduzierten Mikroabriebs an Quarzglas zu erhal-
ten. Dazu wurde die in-situ-Auswertung der Querkraft und des Reibungsko-
e�zienten mit der mit der postmortalen optischen Inspektion nach dem Vor-
wärtskratzen mit einem Berkovich-Eindringkörper verglichen. Die statistis-
che Analyse ergab zwei zugrunde liegende Wahrscheinlichkeitsfunktionen für
das Auftreten von Mikroabrieb, d.h. die Wahrscheinlichkeit dass der sich
ausbreitende Kratzer eine Ober�ächenfehlstelle tri�t und die Wahrschein-
lichkeit, dass ein solches Ereignis einen beobachtbaren Mikroriss verursacht.
Die Dominanz des Erstere folgt einer Exponentialfunktion, die eine reine Zu-
fallsverteilung mit lastunabhängiger Ausfallwahrscheinlichkeit widerspiegelt.
Sie wurde nur bei hohen Kratzgeschwindigkeiten nach Überschreiten einer
bestimmten Normallast beobachtet. Für letztere wurde festgestellt, dass
der Weibull-Modul mit zunehmender Kratzgeschwindigkeit Geschwindigkeit,
d.h. von 1,6 auf 4,4. Hier wurde der niedrige Weibull-Modul bei niedriger
Last auf die zunehmende Zeit der lokalen Dehnung zurückgeführt, was zu
einer Verringerung der der Lastabhängigkeit der Mikrorissbildung führt. Für
Siliziumdioxid und unter Verwendung dem vorliegenden experimentellen Ansatz
liegt die kritische laterale Last für Mikroabrasion (50. Perzentil) bei etwa
30-40 mN. Dieser Wert ist sehr wahrscheinlich abhängig von extrinsischen
Parametern wie der Umgebungsfeuchte abhängig.
Des Weiteren wurde die Rampenlast-Ritztechnik verwendet, um tribolo-
gische Informationen über die Ober�äche des metallischen Glases (Zr55Cu30Al10Ni5)
zu erhalten, die ein groÿes Potential für industrielle Anwendungen hat. Auch
hier wurde bestätigt, dass das Kratzen ein stärkerer Verformungsmodus im
Vergleich zur normaler Eindrückung ist. Dies wurde durch die Untersuchung
der ersten pop-in auf P-h-Diagramme argumentiert. Der aus den Eindring-
daten geschätzte Reibungskoe�zient lag zwischen 0 und 0,15, also genau
zwischen den Reibungskoe�zienten von Gläsern und Metallen. Eine weit-
ere rasterelektronenmikroskopische Untersuchung der Kratzer auf der Ober-
�äche zeigte, dass es möglicherweise einen Zusammenhang zwischen dem Be-
ginn der Scherdeformation Verformung und den halbkreisförmigen Mustern,
die auf der Ober�äche beobachtet wurden.
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Appendix
Derivation of equation 4.2 in the main text In the most basic approx-
imation the nanoindenter tip can be modelled as a rigid object of mass m
which is pulled laterally (with constant velocity v) by a spring of sti�ness k.
If Fs is the static friction force, the tip will not move till the time
t1 =Fs
kv(E1)
At this point, the tip will respond as a harmonic oscillator subjected to
a negative (kinetic) friction force Fk (< Fs) slowing it down. The equation
of motion can be easily solved giving
x(t) = vt− Fk
k− a sin(ω0t+ ϕ) (E2)
for the tip position along the surface. In eq. E2 ω0 = (k/m)1/2 is the
resonance frequency of the spring+tip system. The oscillation amplitude a
and the phase shift ϕ are given by
a = (v2
ω2+
(Fs − Fk)2
k2)1/2 (E3)
109
110 Appendix
Figure F1: (a) Width and (b) depth of the wear grooves formed on a silica
glass surface scratched by a Berkovich diamond tip with a scan velocity of
10 µm/s and di�erent normal loads.
Figure F2: (a) AFM topography corresponding to Fig. 4.10(a); (b) horizon-
tal cross-section along the blue line in (a).
Appendix 111
Figure F3: AFM topography of the very end of the scratch. Frame size: 14.1
µm∗6.1 µm.
Figure F4: (a) AFM topography of one section of scratch performed at load
of 30 mN. (b) Pro�le along the scratch shown with a horizontal line in (a).
(c) FFT analysis of the same image. (d) Pro�le along the line in (c).
112
Selbststii ndigkeitserkliirun g
Ich erkliire, dass ich die vorliegende Arbeit selbststiindig und unter Verwendungder angegebenen Hilfsmiuel, persdnlichen Mitteilungen und Quellen angefertigthabe.
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//'ortqz ll! L" v
Elham Moayedi
113